First pass to homgenize notation for transpose (**T) and conjugate transpose (**H)

Corresponds to bug0024

610 files changed, 2894 insertions, 2889 deletions

diff --git a/SRC/cgbbrd.f b/SRC/cgbbrd.f
index 4de53667..fc47ca86 100644
--- a/SRC/cgbbrd.f
+++ b/SRC/cgbbrd.f
@@ -20,20 +20,20 @@
 *  =======
 *
 *  CGBBRD reduces a complex general m-by-n band matrix A to real upper
-*  bidiagonal form B by a unitary transformation: Q' * A * P = B.
+*  bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 *
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
+*  The routine computes B, and optionally forms Q or P**H, or computes
+*  Q**H*C for a given matrix C.
 *
 *  Arguments
 *  =========
 *
 *  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
+*          Specifies whether or not the matrices Q and P**H are to be
 *          formed.
-*          = 'N': do not form Q or P';
+*          = 'N': do not form Q or P**H;
 *          = 'Q': form Q only;
-*          = 'P': form P' only;
+*          = 'P': form P**H only;
 *          = 'B': form both.
 *
 *  M       (input) INTEGER
@@ -86,7 +86,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,NCC)
 *          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
+*          On exit, C is overwritten by Q**H*C.
 *          C is not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
@@ -165,7 +165,7 @@
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**H to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL CLASET( 'Full', M, M, CZERO, CONE, Q, LDQ )
@@ -338,7 +338,7 @@
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**H
 *
                   DO 60 J = J1, J2, KB1
                      CALL CROT( N, PT( J+KUN-1, 1 ), LDPT,
diff --git a/SRC/cgbcon.f b/SRC/cgbcon.f
index 8acd43a6..0493c0ff 100644
--- a/SRC/cgbcon.f
+++ b/SRC/cgbcon.f
@@ -187,13 +187,13 @@
      $                   KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             IF( LNOTI ) THEN
                DO 30 J = N - 1, 1, -1
diff --git a/SRC/cgebd2.f b/SRC/cgebd2.f
index d1148a15..6d85c003 100644
--- a/SRC/cgebd2.f
+++ b/SRC/cgebd2.f
@@ -87,7 +87,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, v and u are complex vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
@@ -170,7 +170,7 @@
             D( I ) = ALPHA
             A( I, I ) = ONE
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             IF( I.LT.N )
      $         CALL CLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
@@ -233,7 +233,7 @@
                E( I ) = ALPHA
                A( I+1, I ) = ONE
 *
-*              Apply H(i)' to A(i+1:m,i+1:n) from the left
+*              Apply H(i)**H to A(i+1:m,i+1:n) from the left
 *
                CALL CLARF( 'Left', M-I, N-I, A( I+1, I ), 1,
      $                     CONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA,
diff --git a/SRC/cgebrd.f b/SRC/cgebrd.f
index 72749e3c..06c95fb1 100644
--- a/SRC/cgebrd.f
+++ b/SRC/cgebrd.f
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -113,7 +113,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
@@ -233,7 +233,7 @@
      $                WORK( LDWRKX*NB+1 ), LDWRKY )
 *
 *        Update the trailing submatrix A(i+ib:m,i+ib:n), using
-*        an update of the form  A := A - V*Y' - X*U'
+*        an update of the form  A := A - V*Y**H - X*U**H
 *
          CALL CGEMM( 'No transpose', 'Conjugate transpose', M-I-NB+1,
      $               N-I-NB+1, NB, -ONE, A( I+NB, I ), LDA,
diff --git a/SRC/cgecon.f b/SRC/cgecon.f
index de14d318..affb98b7 100644
--- a/SRC/cgecon.f
+++ b/SRC/cgecon.f
@@ -156,13 +156,13 @@
      $                   A, LDA, WORK, SU, RWORK( N+1 ), INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SU, RWORK( N+1 ),
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL CLATRS( 'Lower', 'Conjugate transpose', 'Unit', NORMIN,
      $                   N, A, LDA, WORK, SL, RWORK, INFO )
diff --git a/SRC/cgehd2.f b/SRC/cgehd2.f
index 9237dca8..866ff472 100644
--- a/SRC/cgehd2.f
+++ b/SRC/cgehd2.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  CGEHD2 reduces a complex general matrix A to upper Hessenberg form H
-*  by a unitary similarity transformation:  Q' * A * Q = H .
+*  by a unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -63,7 +63,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -134,7 +134,7 @@
          CALL CLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
      $               A( 1, I+1 ), LDA, WORK )
 *
-*        Apply H(i)' to A(i+1:ihi,i+1:n) from the left
+*        Apply H(i)**H to A(i+1:ihi,i+1:n) from the left
 *
          CALL CLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1,
      $               CONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK )
diff --git a/SRC/cgehrd.f b/SRC/cgehrd.f
index 6f7f9855..8cf805d9 100644
--- a/SRC/cgehrd.f
+++ b/SRC/cgehrd.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  CGEHRD reduces a complex general matrix A to upper Hessenberg form H by
-*  an unitary similarity transformation:  Q' * A * Q = H .
+*  an unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -223,14 +223,14 @@
             IB = MIN( NB, IHI-I )
 *
 *           Reduce columns i:i+ib-1 to Hessenberg form, returning the
-*           matrices V and T of the block reflector H = I - V*T*V'
+*           matrices V and T of the block reflector H = I - V*T*V**H
 *           which performs the reduction, and also the matrix Y = A*V*T
 *
             CALL CLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
      $                   WORK, LDWORK )
 *
 *           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
+*           right, computing  A := A - Y * V**H. V(i+ib,ib-1) must be set
 *           to 1
 *
             EI = A( I+IB, I+IB-1 )
diff --git a/SRC/cgelq2.f b/SRC/cgelq2.f
index ae39d8dc..c513d496 100644
--- a/SRC/cgelq2.f
+++ b/SRC/cgelq2.f
@@ -53,11 +53,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
diff --git a/SRC/cgelqf.f b/SRC/cgelqf.f
index 0c90359b..06a60975 100644
--- a/SRC/cgelqf.f
+++ b/SRC/cgelqf.f
@@ -64,11 +64,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
diff --git a/SRC/cgels.f b/SRC/cgels.f
index 646d6e89..3fd0e065 100644
--- a/SRC/cgels.f
+++ b/SRC/cgels.f
@@ -278,7 +278,7 @@
 *
 *           Least-Squares Problem min || A * X - B ||
 *
-*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
             CALL CUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
@@ -360,7 +360,7 @@
    30          CONTINUE
    40       CONTINUE
 *
-*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS)
+*           B(1:N,1:NRHS) := Q(1:N,:)**H * B(1:M,1:NRHS)
 *
             CALL CUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
diff --git a/SRC/cgelsx.f b/SRC/cgelsx.f
index b321bc6c..1642ea80 100644
--- a/SRC/cgelsx.f
+++ b/SRC/cgelsx.f
@@ -45,8 +45,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**H [ inv(T11)*Q1**H*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  Arguments
@@ -275,7 +275,7 @@
 *
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
       CALL CUNM2R( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA,
      $             WORK( 1 ), B, LDB, WORK( 2*MN+1 ), INFO )
@@ -293,7 +293,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          DO 50 I = 1, RANK
diff --git a/SRC/cgelsy.f b/SRC/cgelsy.f
index e0da0be2..636b1709 100644
--- a/SRC/cgelsy.f
+++ b/SRC/cgelsy.f
@@ -319,7 +319,7 @@
 *     complex workspace: 2*MN.
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
       CALL CUNMQR( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA,
      $             WORK( 1 ), B, LDB, WORK( 2*MN+1 ), LWORK-2*MN, INFO )
@@ -338,7 +338,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          CALL CUNMRZ( 'Left', 'Conjugate transpose', N, NRHS, RANK,
diff --git a/SRC/cgeql2.f b/SRC/cgeql2.f
index 2e7c31a6..d42fae13 100644
--- a/SRC/cgeql2.f
+++ b/SRC/cgeql2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -108,7 +108,7 @@
          ALPHA = A( M-K+I, N-K+I )
          CALL CLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
 *
-*        Apply H(i)' to A(1:m-k+i,1:n-k+i-1) from the left
+*        Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
 *
          A( M-K+I, N-K+I ) = ONE
          CALL CLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1,
diff --git a/SRC/cgeqlf.f b/SRC/cgeqlf.f
index 340f7c25..c99a4b26 100644
--- a/SRC/cgeqlf.f
+++ b/SRC/cgeqlf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -186,7 +186,7 @@
                CALL CLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
      $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
+*              Apply H**H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
 *
                CALL CLARFB( 'Left', 'Conjugate transpose', 'Backward',
      $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
diff --git a/SRC/cgeqp3.f b/SRC/cgeqp3.f
index e97c55a0..d70f613e 100644
--- a/SRC/cgeqp3.f
+++ b/SRC/cgeqp3.f
@@ -79,7 +79,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a real/complex scalar, and v is a real/complex vector
 *  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
diff --git a/SRC/cgeqpf.f b/SRC/cgeqpf.f
index c438538c..3ff29843 100644
--- a/SRC/cgeqpf.f
+++ b/SRC/cgeqpf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H = I - tau * v * v'
+*     H = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
diff --git a/SRC/cgeqr2.f b/SRC/cgeqr2.f
index 9123ba15..28c0b994 100644
--- a/SRC/cgeqr2.f
+++ b/SRC/cgeqr2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -106,7 +106,7 @@
      $                TAU( I ) )
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             ALPHA = A( I, I )
             A( I, I ) = ONE
diff --git a/SRC/cgeqr2p.f b/SRC/cgeqr2p.f
index a869fbae..59841041 100644
--- a/SRC/cgeqr2p.f
+++ b/SRC/cgeqr2p.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -106,7 +106,7 @@
      $                TAU( I ) )
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             ALPHA = A( I, I )
             A( I, I ) = ONE
diff --git a/SRC/cgeqrf.f b/SRC/cgeqrf.f
index 01d2af1d..b5f303b6 100644
--- a/SRC/cgeqrf.f
+++ b/SRC/cgeqrf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL CLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**H to A(i:m,i+ib:n) from the left
 *
                CALL CLARFB( 'Left', 'Conjugate transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/cgeqrfp.f b/SRC/cgeqrfp.f
index 9f96f7dc..26dd05dc 100644
--- a/SRC/cgeqrfp.f
+++ b/SRC/cgeqrfp.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL CLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**H to A(i:m,i+ib:n) from the left
 *
                CALL CLARFB( 'Left', 'Conjugate transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/cgerq2.f b/SRC/cgerq2.f
index 574aa7ed..c900b35f 100644
--- a/SRC/cgerq2.f
+++ b/SRC/cgerq2.f
@@ -55,11 +55,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
+*     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
diff --git a/SRC/cgerqf.f b/SRC/cgerqf.f
index 04e7f530..cf03cde0 100644
--- a/SRC/cgerqf.f
+++ b/SRC/cgerqf.f
@@ -67,11 +67,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
+*     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
diff --git a/SRC/cgetrs.f b/SRC/cgetrs.f
index 2b85559e..62bb3a08 100644
--- a/SRC/cgetrs.f
+++ b/SRC/cgetrs.f
@@ -128,12 +128,12 @@
 *
 *        Solve A**T * X = B  or A**H * X = B.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B or U**H *X = B, overwriting B with X.
 *
          CALL CTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE,
      $               A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, or L**H *X = B overwriting B with X.
 *
          CALL CTRSM( 'Left', 'Lower', TRANS, 'Unit', N, NRHS, ONE, A,
      $               LDA, B, LDB )
diff --git a/SRC/cggglm.f b/SRC/cggglm.f
index 7bc72af5..9e738cc8 100644
--- a/SRC/cggglm.f
+++ b/SRC/cggglm.f
@@ -187,9 +187,9 @@
 *
 *     Compute the GQR factorization of matrices A and B:
 *
-*            Q'*A = ( R11 ) M,    Q'*B*Z' = ( T11   T12 ) M
-*                   (  0  ) N-M             (  0    T22 ) N-M
-*                      M                     M+P-N  N-M
+*          Q**H*A = ( R11 ) M,    Q**H*B*Z**H = ( T11   T12 ) M
+*                   (  0  ) N-M                 (  0    T22 ) N-M
+*                      M                         M+P-N  N-M
 *
 *     where R11 and T22 are upper triangular, and Q and Z are
 *     unitary.
@@ -198,8 +198,8 @@
      $             WORK( M+NP+1 ), LWORK-M-NP, INFO )
       LOPT = WORK( M+NP+1 )
 *
-*     Update left-hand-side vector d = Q'*d = ( d1 ) M
-*                                             ( d2 ) N-M
+*     Update left-hand-side vector d = Q**H*d = ( d1 ) M
+*                                               ( d2 ) N-M
 *
       CALL CUNMQR( 'Left', 'Conjugate transpose', N, 1, M, A, LDA, WORK,
      $             D, MAX( 1, N ), WORK( M+NP+1 ), LWORK-M-NP, INFO )
@@ -246,7 +246,7 @@
          CALL CCOPY( M, D, 1, X, 1 )
       END IF
 *
-*     Backward transformation y = Z'*y
+*     Backward transformation y = Z**H *y
 *
       CALL CUNMRQ( 'Left', 'Conjugate transpose', P, 1, NP,
      $             B( MAX( 1, N-P+1 ), 1 ), LDB, WORK( M+1 ), Y,
diff --git a/SRC/cgglse.f b/SRC/cgglse.f
index 43984c96..e3614017 100644
--- a/SRC/cgglse.f
+++ b/SRC/cgglse.f
@@ -183,9 +183,9 @@
 *
 *     Compute the GRQ factorization of matrices B and A:
 *
-*            B*Q' = (  0  T12 ) P   Z'*A*Q' = ( R11 R12 ) N-P
-*                     N-P  P                  (  0  R22 ) M+P-N
-*                                               N-P  P
+*            B*Q**H = (  0  T12 ) P   Z**H*A*Q**H = ( R11 R12 ) N-P
+*                        N-P  P                     (  0  R22 ) M+P-N
+*                                                      N-P  P
 *
 *     where T12 and R11 are upper triangular, and Q and Z are
 *     unitary.
@@ -194,7 +194,7 @@
      $             WORK( P+MN+1 ), LWORK-P-MN, INFO )
       LOPT = WORK( P+MN+1 )
 *
-*     Update c = Z'*c = ( c1 ) N-P
+*     Update c = Z**H *c = ( c1 ) N-P
 *                       ( c2 ) M+P-N
 *
       CALL CUNMQR( 'Left', 'Conjugate Transpose', M, 1, MN, A, LDA,
@@ -255,7 +255,7 @@
          CALL CAXPY( NR, -CONE, D, 1, C( N-P+1 ), 1 )
       END IF
 *
-*     Backward transformation x = Q'*x
+*     Backward transformation x = Q**H*x
 *
       CALL CUNMRQ( 'Left', 'Conjugate Transpose', N, 1, P, B, LDB,
      $             WORK( 1 ), X, N, WORK( P+MN+1 ), LWORK-P-MN, INFO )
diff --git a/SRC/cggqrf.f b/SRC/cggqrf.f
index d409bfbf..7f8fb74c 100644
--- a/SRC/cggqrf.f
+++ b/SRC/cggqrf.f
@@ -40,7 +40,7 @@
 *  In particular, if B is square and nonsingular, the GQR factorization
 *  of A and B implicitly gives the QR factorization of inv(B)*A:
 *
-*               inv(B)*A = Z'*(inv(T)*R)
+*               inv(B)*A = Z**H * (inv(T)*R)
 *
 *  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
 *  conjugate transpose of matrix Z.
@@ -119,7 +119,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**H
 *
 *  where taua is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -133,7 +133,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**H
 *
 *  where taub is a complex scalar, and v is a complex vector with
 *  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
@@ -194,7 +194,7 @@
       CALL CGEQRF( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := Q'*B.
+*     Update B := Q**H*B.
 *
       CALL CUNMQR( 'Left', 'Conjugate Transpose', N, P, MIN( N, M ), A,
      $             LDA, TAUA, B, LDB, WORK, LWORK, INFO )
diff --git a/SRC/cggrqf.f b/SRC/cggrqf.f
index 5ed04080..51f39734 100644
--- a/SRC/cggrqf.f
+++ b/SRC/cggrqf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GRQ factorization
 *  of A and B implicitly gives the RQ factorization of A*inv(B):
 *
-*               A*inv(B) = (R*inv(T))*Z'
+*               A*inv(B) = (R*inv(T))*Z**H
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
 *  conjugate transpose of the matrix Z.
 *
 *  Arguments
@@ -118,7 +118,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**H
 *
 *  where taua is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
@@ -132,7 +132,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**H
 *
 *  where taub is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
@@ -193,7 +193,7 @@
       CALL CGERQF( M, N, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := B*Q'
+*     Update B := B*Q**H
 *
       CALL CUNMRQ( 'Right', 'Conjugate Transpose', P, N, MIN( M, N ),
      $             A( MAX( 1, M-N+1 ), 1 ), LDA, TAUA, B, LDB, WORK,
diff --git a/SRC/cggsvd.f b/SRC/cggsvd.f
index 0396e584..e8306976 100644
--- a/SRC/cggsvd.f
+++ b/SRC/cggsvd.f
@@ -24,11 +24,11 @@
 *  CGGSVD computes the generalized singular value decomposition (GSVD)
 *  of an M-by-N complex matrix A and P-by-N complex matrix B:
 *
-*        U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R )
+*        U**H*A*Q = D1*( 0 R ),    V**H*B*Q = D2*( 0 R )
 *
-*  where U, V and Q are unitary matrices, and Z' means the conjugate
-*  transpose of Z.  Let K+L = the effective numerical rank of the
-*  matrix (A',B')', then R is a (K+L)-by-(K+L) nonsingular upper
+*  where U, V and Q are unitary matrices.
+*  Let K+L = the effective numerical rank of the
+*  matrix (A**H,B**H)**H, then R is a (K+L)-by-(K+L) nonsingular upper
 *  triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal"
 *  matrices and of the following structures, respectively:
 *
@@ -46,6 +46,7 @@
 *                  N-K-L  K    L
 *    ( 0 R ) = K (  0   R11  R12 )
 *              L (  0    0   R22 )
+*
 *  where
 *
 *    C = diag( ALPHA(K+1), ... , ALPHA(K+L) ),
@@ -85,13 +86,13 @@
 *
 *  In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
 *  A and B implicitly gives the SVD of A*inv(B):
-*                       A*inv(B) = U*(D1*inv(D2))*V'.
-*  If ( A',B')' has orthnormal columns, then the GSVD of A and B is also
+*                       A*inv(B) = U*(D1*inv(D2))*V**H.
+*  If ( A**H,B**H)**H has orthnormal columns, then the GSVD of A and B is also
 *  equal to the CS decomposition of A and B. Furthermore, the GSVD can
 *  be used to derive the solution of the eigenvalue problem:
-*                       A'*A x = lambda* B'*B x.
+*                       A**H*A x = lambda* B**H*B x.
 *  In some literature, the GSVD of A and B is presented in the form
-*                   U'*A*X = ( 0 D1 ),   V'*B*X = ( 0 D2 )
+*                   U**H*A*X = ( 0 D1 ),   V**H*B*X = ( 0 D2 )
 *  where U and V are orthogonal and X is nonsingular, and D1 and D2 are
 *  ``diagonal''.  The former GSVD form can be converted to the latter
 *  form by taking the nonsingular matrix X as
@@ -127,7 +128,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in Purpose.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**H,B**H)**H.
 *
 *  A       (input/output) COMPLEX array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
@@ -209,7 +210,7 @@
 *  TOLA    REAL
 *  TOLB    REAL
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')'. Generally, they are set to
+*          rank of (A',B')**H. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MACHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MACHEPS.
 *          The size of TOLA and TOLB may affect the size of backward
diff --git a/SRC/cggsvp.f b/SRC/cggsvp.f
index e4aa67cf..f194cbdb 100644
--- a/SRC/cggsvp.f
+++ b/SRC/cggsvp.f
@@ -24,24 +24,23 @@
 *
 *  CGGSVP computes unitary matrices U, V and Q such that
 *
-*                   N-K-L  K    L
-*   U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
-*                L ( 0     0   A23 )
-*            M-K-L ( 0     0    0  )
+*                     N-K-L  K    L
+*   U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
+*                  L ( 0     0   A23 )
+*              M-K-L ( 0     0    0  )
 *
 *                   N-K-L  K    L
 *          =     K ( 0    A12  A13 )  if M-K-L < 0;
 *              M-K ( 0     0   A23 )
 *
-*                 N-K-L  K    L
-*   V'*B*Q =   L ( 0     0   B13 )
-*            P-L ( 0     0    0  )
+*                   N-K-L  K    L
+*   V**H*B*Q =   L ( 0     0   B13 )
+*              P-L ( 0     0    0  )
 *
 *  where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 *  upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 *  otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
-*  numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the
-*  conjugate transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -101,7 +100,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**H,B**H)**H.
 *
 *  U       (output) COMPLEX array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the unitary matrix U.
@@ -268,13 +267,13 @@
 *
          CALL CGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**H
 *
          CALL CUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB,
      $                TAU, A, LDA, WORK, INFO )
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**H
 *
             CALL CUNMR2( 'Right', 'Conjugate transpose', N, N, L, B,
      $                   LDB, TAU, Q, LDQ, WORK, INFO )
@@ -296,7 +295,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**H
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -312,7 +311,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL CUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ),
      $             A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -354,7 +353,7 @@
 *
          IF( WANTQ ) THEN
 *
-*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1'
+*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**H
 *
             CALL CUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A,
      $                   LDA, TAU, Q, LDQ, WORK, INFO )
diff --git a/SRC/cgtcon.f b/SRC/cgtcon.f
index a2791840..67d478bd 100644
--- a/SRC/cgtcon.f
+++ b/SRC/cgtcon.f
@@ -152,7 +152,7 @@
      $                   WORK, N, INFO )
          ELSE
 *
-*           Multiply by inv(L')*inv(U').
+*           Multiply by inv(L**H)*inv(U**H).
 *
             CALL CGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
      $                   IPIV, WORK, N, INFO )
diff --git a/SRC/cgtsv.f b/SRC/cgtsv.f
index 4dc3c47b..40c857f1 100644
--- a/SRC/cgtsv.f
+++ b/SRC/cgtsv.f
@@ -22,7 +22,7 @@
 *  where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
 *  partial pivoting.
 *
-*  Note that the equation  A'*X = B  may be solved by interchanging the
+*  Note that the equation  A**H *X = B  may be solved by interchanging the
 *  order of the arguments DU and DL.
 *
 *  Arguments
diff --git a/SRC/checon.f b/SRC/checon.f
index 226c17ac..a4e0e920 100644
--- a/SRC/checon.f
+++ b/SRC/checon.f
@@ -146,7 +146,7 @@
       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
 *
          CALL CHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/chegs2.f b/SRC/chegs2.f
index f88631f0..ebaaf909 100644
--- a/SRC/chegs2.f
+++ b/SRC/chegs2.f
@@ -20,19 +20,19 @@
 *  eigenproblem to standard form.
 *
 *  If ITYPE = 1, the problem is A*x = lambda*B*x,
-*  and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
+*  and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
 *
 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-*  B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
+*  B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
 *
-*  B must have been previously factorized as U'*U or L*L' by CPOTRF.
+*  B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
 *
 *  Arguments
 *  =========
 *
 *  ITYPE   (input) INTEGER
-*          = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
-*          = 2 or 3: compute U*A*U' or L'*A*L.
+*          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
+*          = 2 or 3: compute U*A*U**H or L**H *A*L.
 *
 *  UPLO    (input) CHARACTER*1
 *          Specifies whether the upper or lower triangular part of the
@@ -119,7 +119,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**H)*A*inv(U)
 *
             DO 10 K = 1, N
 *
@@ -149,7 +149,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**H)
 *
             DO 20 K = 1, N
 *
@@ -174,7 +174,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**H
 *
             DO 30 K = 1, N
 *
@@ -194,7 +194,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**H *A*L
 *
             DO 40 K = 1, N
 *
diff --git a/SRC/chegst.f b/SRC/chegst.f
index 10a2c264..c61bd36a 100644
--- a/SRC/chegst.f
+++ b/SRC/chegst.f
@@ -136,7 +136,7 @@
          IF( ITYPE.EQ.1 ) THEN
             IF( UPPER ) THEN
 *
-*              Compute inv(U')*A*inv(U)
+*              Compute inv(U**H)*A*inv(U)
 *
                DO 10 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -167,7 +167,7 @@
    10          CONTINUE
             ELSE
 *
-*              Compute inv(L)*A*inv(L')
+*              Compute inv(L)*A*inv(L**H)
 *
                DO 20 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -200,7 +200,7 @@
          ELSE
             IF( UPPER ) THEN
 *
-*              Compute U*A*U'
+*              Compute U*A*U**H
 *
                DO 30 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -226,7 +226,7 @@
    30          CONTINUE
             ELSE
 *
-*              Compute L'*A*L
+*              Compute L**H*A*L
 *
                DO 40 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
diff --git a/SRC/chegv.f b/SRC/chegv.f
index d8e45a75..6d5c4a30 100644
--- a/SRC/chegv.f
+++ b/SRC/chegv.f
@@ -197,7 +197,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -211,7 +211,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H*y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chegvd.f b/SRC/chegvd.f
index 61ee89a4..7d0362a6 100644
--- a/SRC/chegvd.f
+++ b/SRC/chegvd.f
@@ -270,7 +270,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -284,7 +284,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chegvx.f b/SRC/chegvx.f
index eb6b8756..c07a8299 100644
--- a/SRC/chegvx.f
+++ b/SRC/chegvx.f
@@ -299,7 +299,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -313,7 +313,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H*y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chesv.f b/SRC/chesv.f
index 2705bb52..5e59ca44 100644
--- a/SRC/chesv.f
+++ b/SRC/chesv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
       CALL CHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/chesvx.f b/SRC/chesvx.f
index ea0c5e2f..2a22358f 100644
--- a/SRC/chesvx.f
+++ b/SRC/chesvx.f
@@ -255,7 +255,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
          CALL CLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL CHETRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/chetd2.f b/SRC/chetd2.f
index 89eb1e90..541ac522 100644
--- a/SRC/chetd2.f
+++ b/SRC/chetd2.f
@@ -19,7 +19,7 @@
 *
 *  CHETD2 reduces a complex Hermitian matrix A to real symmetric
 *  tridiagonal form T by a unitary similarity transformation:
-*  Q' * A * Q = T.
+*  Q**H * A * Q = T.
 *
 *  Arguments
 *  =========
@@ -81,7 +81,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -94,7 +94,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -168,7 +168,7 @@
          A( N, N ) = REAL( A( N, N ) )
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(1:i-1,i+1)
 *
             ALPHA = A( I, I+1 )
@@ -186,13 +186,13 @@
                CALL CHEMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
      $                     TAU, 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**H * v) * v
 *
                ALPHA = -HALF*TAUI*CDOTC( I, TAU, 1, A( 1, I+1 ), 1 )
                CALL CAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**H - w * v**H
 *
                CALL CHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
      $                     LDA )
@@ -212,7 +212,7 @@
          A( 1, 1 ) = REAL( A( 1, 1 ) )
          DO 20 I = 1, N - 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(i+2:n,i)
 *
             ALPHA = A( I+1, I )
@@ -230,14 +230,14 @@
                CALL CHEMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
      $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**H * v) * v
 *
                ALPHA = -HALF*TAUI*CDOTC( N-I, TAU( I ), 1, A( I+1, I ),
      $                 1 )
                CALL CAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**H
 *
                CALL CHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )
diff --git a/SRC/chetf2.f b/SRC/chetf2.f
index 99c11509..5d41a374 100644
--- a/SRC/chetf2.f
+++ b/SRC/chetf2.f
@@ -20,10 +20,10 @@
 *  CHETF2 computes the factorization of a complex Hermitian matrix A
 *  using the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**H  or  A = L*D*L**H
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the conjugate transpose of U, and D is
+*  triangular matrices, U**H is the conjugate transpose of U, and D is
 *  Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -88,7 +88,7 @@
 *    J. Lewis, Boeing Computer Services Company
 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -105,7 +105,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -179,7 +179,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -296,7 +296,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H
 *
                R1 = ONE / REAL( A( K, K ) )
                CALL CHER( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -315,8 +315,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H
 *
                IF( K.GT.2 ) THEN
 *
@@ -361,7 +361,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -481,7 +481,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H
 *
                   R1 = ONE / REAL( A( K, K ) )
                   CALL CHER( UPLO, N-K, -R1, A( K+1, K ), 1,
@@ -499,8 +499,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/chetrd.f b/SRC/chetrd.f
index 367aca1a..2868958c 100644
--- a/SRC/chetrd.f
+++ b/SRC/chetrd.f
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -105,7 +105,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -237,7 +237,7 @@
      $                   LDWORK )
 *
 *           Update the unreduced submatrix A(1:i-1,1:i-1), using an
-*           update of the form:  A := A - V*W' - W*V'
+*           update of the form:  A := A - V*W' - W*V**H
 *
             CALL CHER2K( UPLO, 'No transpose', I-1, NB, -CONE,
      $                   A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA )
@@ -268,7 +268,7 @@
      $                   TAU( I ), WORK, LDWORK )
 *
 *           Update the unreduced submatrix A(i+nb:n,i+nb:n), using
-*           an update of the form:  A := A - V*W' - W*V'
+*           an update of the form:  A := A - V*W' - W*V**H
 *
             CALL CHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE,
      $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
diff --git a/SRC/chetrf.f b/SRC/chetrf.f
index c9b94ad2..ad6ad54e 100644
--- a/SRC/chetrf.f
+++ b/SRC/chetrf.f
@@ -82,7 +82,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -99,7 +99,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -182,7 +182,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by CLAHEF;
@@ -222,7 +222,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by CLAHEF;
diff --git a/SRC/chetri.f b/SRC/chetri.f
index 6160f600..582c4822 100644
--- a/SRC/chetri.f
+++ b/SRC/chetri.f
@@ -130,7 +130,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -225,7 +225,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/chetri2x.f b/SRC/chetri2x.f
index 6a01d5d2..9bafd618 100644
--- a/SRC/chetri2x.f
+++ b/SRC/chetri2x.f
@@ -156,7 +156,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
 *
         CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -184,9 +184,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**H) = (inv(U))**H
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**H)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -311,7 +311,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -333,7 +333,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
 *
          CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -361,9 +361,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**H) = (inv(U))**H
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**H)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -494,7 +494,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/chetrs.f b/SRC/chetrs.f
index 9decc888..a7767c07 100644
--- a/SRC/chetrs.f
+++ b/SRC/chetrs.f
@@ -108,7 +108,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -180,7 +180,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -197,7 +197,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**H(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.GT.1 ) THEN
@@ -217,7 +217,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             IF( K.GT.1 ) THEN
@@ -245,7 +245,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -320,7 +320,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -337,7 +337,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**H(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N ) THEN
@@ -358,7 +358,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/chetrs2.f b/SRC/chetrs2.f
index 72a9559f..90ea8019 100644
--- a/SRC/chetrs2.f
+++ b/SRC/chetrs2.f
@@ -21,9 +21,9 @@
 *  Purpose
 *  =======
 *
-*  CHETRS2 solves a system of linear equations A*X = B with a COMPLEX
-*  Hermitian matrix A using the factorization A = U*D*U**T or
-*  A = L*D*L**T computed by CSYTRF and converted by CSYCONV.
+*  CHETRS2 solves a system of linear equations A*X = B with a complex
+*  Hermitian matrix A using the factorization A = U*D*U**H or
+*  A = L*D*L**H computed by CHETRF and converted by CSYCONV.
 *
 *  Arguments
 *  =========
@@ -118,9 +118,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
-*       P' * B  
+*       P**T * B  
         K=N
         DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN
@@ -140,11 +140,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL CTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -169,11 +169,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**H \ B) -> B   [ U**H \ (D \ (U \P**T * B) ) ]
 *
          CALL CTRSM('L','U','C','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**H \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -196,9 +196,9 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
-*       P' * B  
+*       P**T * B  
         K=1
         DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN
@@ -218,11 +218,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL CTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -245,11 +245,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**H \ B) -> B   [ L**H \ (D \ (L \P**T * B) ) ]
 * 
         CALL CTRSM('L','L','C','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**H \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/chpcon.f b/SRC/chpcon.f
index c83a0ed9..cae21d02 100644
--- a/SRC/chpcon.f
+++ b/SRC/chpcon.f
@@ -142,7 +142,7 @@
       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
 *
          CALL CHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/chpgst.f b/SRC/chpgst.f
index acc6acf2..f3b607a5 100644
--- a/SRC/chpgst.f
+++ b/SRC/chpgst.f
@@ -108,7 +108,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**H)*A*inv(U)
 *
 *           J1 and JJ are the indices of A(1,j) and A(j,j)
 *
@@ -131,7 +131,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**H)
 *
 *           KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
 *
@@ -161,7 +161,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**H
 *
 *           K1 and KK are the indices of A(1,k) and A(k,k)
 *
@@ -186,7 +186,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**H *A*L
 *
 *           JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
 *
diff --git a/SRC/chpgv.f b/SRC/chpgv.f
index 8973bbf5..727768a3 100644
--- a/SRC/chpgv.f
+++ b/SRC/chpgv.f
@@ -160,7 +160,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -176,7 +176,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H*y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chpgvd.f b/SRC/chpgvd.f
index f7eb424c..4a55b7bc 100644
--- a/SRC/chpgvd.f
+++ b/SRC/chpgvd.f
@@ -203,10 +203,10 @@
                LIWMIN = 1
             END IF
          END IF
+*
          WORK( 1 ) = LWMIN
          RWORK( 1 ) = LRWMIN
          IWORK( 1 ) = LIWMIN
-*
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -11
          ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
@@ -255,7 +255,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -271,7 +271,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chpgvx.f b/SRC/chpgvx.f
index 1f01775e..910fd963 100644
--- a/SRC/chpgvx.f
+++ b/SRC/chpgvx.f
@@ -256,7 +256,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -272,7 +272,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H*y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/chpsv.f b/SRC/chpsv.f
index fcb5d1ca..7ff3dc15 100644
--- a/SRC/chpsv.f
+++ b/SRC/chpsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
       CALL CHPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/chpsvx.f b/SRC/chpsvx.f
index 390b2c83..d5a6b12c 100644
--- a/SRC/chpsvx.f
+++ b/SRC/chpsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
          CALL CCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL CHPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/chptrd.f b/SRC/chptrd.f
index eeb80e0a..82d2fd2f 100644
--- a/SRC/chptrd.f
+++ b/SRC/chptrd.f
@@ -74,7 +74,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
@@ -87,7 +87,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
@@ -147,7 +147,7 @@
          AP( I1+N-1 ) = REAL( AP( I1+N-1 ) )
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(1:i-1,i+1)
 *
             ALPHA = AP( I1+I-1 )
@@ -165,13 +165,13 @@
                CALL CHPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
      $                     1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**H *v) * v
 *
                ALPHA = -HALF*TAUI*CDOTC( I, TAU, 1, AP( I1 ), 1 )
                CALL CAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**H - w * v**H
 *
                CALL CHPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
 *
@@ -192,7 +192,7 @@
          DO 20 I = 1, N - 1
             I1I1 = II + N - I + 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(i+2:n,i)
 *
             ALPHA = AP( II+1 )
@@ -210,14 +210,14 @@
                CALL CHPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
      $                     ZERO, TAU( I ), 1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**H *v) * v
 *
                ALPHA = -HALF*TAUI*CDOTC( N-I, TAU( I ), 1, AP( II+1 ),
      $                 1 )
                CALL CAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**H
 *
                CALL CHPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
      $                     AP( I1I1 ) )
diff --git a/SRC/chptrf.f b/SRC/chptrf.f
index 13846f9c..184d739a 100644
--- a/SRC/chptrf.f
+++ b/SRC/chptrf.f
@@ -71,7 +71,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -88,7 +88,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -161,7 +161,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -293,7 +293,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H
 *
                R1 = ONE / REAL( AP( KC+K-1 ) )
                CALL CHPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -312,8 +312,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H
 *
                IF( K.GT.2 ) THEN
 *
@@ -363,7 +363,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -498,7 +498,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H
 *
                   R1 = ONE / REAL( AP( KC ) )
                   CALL CHPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -521,8 +521,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/chptri.f b/SRC/chptri.f
index d02dca89..e922ac1c 100644
--- a/SRC/chptri.f
+++ b/SRC/chptri.f
@@ -130,7 +130,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -233,7 +233,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/chptrs.f b/SRC/chptrs.f
index 0cfa967c..658e893a 100644
--- a/SRC/chptrs.f
+++ b/SRC/chptrs.f
@@ -104,7 +104,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -179,7 +179,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -197,7 +197,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**H(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.GT.1 ) THEN
@@ -218,7 +218,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             IF( K.GT.1 ) THEN
@@ -247,7 +247,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -325,7 +325,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -344,7 +344,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**H(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N ) THEN
@@ -365,7 +365,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/cla_gbamv.f b/SRC/cla_gbamv.f
index 5773177c..18c765ff 100644
--- a/SRC/cla_gbamv.f
+++ b/SRC/cla_gbamv.f
@@ -10,7 +10,7 @@
 *     -- Univ. of California Berkeley and NAG Ltd.                    --
 *
       IMPLICIT NONE
-*     
+*     ..
 *     .. Scalar Arguments ..
       REAL               ALPHA, BETA
       INTEGER            INCX, INCY, LDAB, M, N, KL, KU, TRANS
@@ -23,10 +23,10 @@
 *  Purpose
 *  =======
 *
-*  SLA_GBAMV  performs one of the matrix-vector operations
+*  CLA_GBAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -48,43 +48,43 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M      (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N      (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  KL     (input) INTEGER
+*  KL       (input) INTEGER
 *           The number of subdiagonals within the band of A.  KL >= 0.
 *
-*  KU     (input) INTEGER
+*  KU       (input) INTEGER
 *           The number of superdiagonals within the band of A.  KU >= 0.
 *
-*  ALPHA  (input) REAL
+*  ALPHA    (input) REAL
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      (input) REAL array, dimension (LDA,n)
-*           Before entry, the leading m by n part of the array A must
+*  AB       (input) REAL array, dimension (LDAB,n)
+*           Before entry, the leading m by n part of the array AB must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA    (input) INTEGER
-*           On entry, LDA specifies the first dimension of A as declared
-*           in the calling (sub) program. LDA must be at least
+*  LDAB     (input) INTEGER
+*           On entry, LDAB specifies the first dimension of AB as declared
+*           in the calling (sub) program. LDAB must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X      (input) REAL array, dimension at least
+*  X        (input) REAL array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -92,17 +92,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX   (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA   (input) REAL
+*  BETA     (input) REAL
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y      (input/output) REAL array, dimension at least
+*  Y        (input/output) REAL array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -110,7 +110,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY   (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/cla_geamv.f b/SRC/cla_geamv.f
index e3593642..927cd87a 100644
--- a/SRC/cla_geamv.f
+++ b/SRC/cla_geamv.f
@@ -27,7 +27,7 @@
 *  CLA_GEAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -49,37 +49,37 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  ALPHA   (input) REAL
+*  ALPHA    (input) REAL
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A       (input) COMPLEX array, dimension (LDA,n)
+*  A        (input) COMPLEX array, dimension (LDA,n)
 *           Before entry, the leading m by n part of the array A must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
+*  LDA      (input) INTEGER
 *           On entry, LDA specifies the first dimension of A as declared
 *           in the calling (sub) program. LDA must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) COMPLEX array, dimension
+*  X        (input) COMPLEX array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -87,17 +87,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA    (input) REAL
+*  BETA     (input) REAL
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y       (input/output) REAL array, dimension
+*  Y        (input/output) REAL array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -105,7 +105,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/clabrd.f b/SRC/clabrd.f
index c96fe003..f731337b 100644
--- a/SRC/clabrd.f
+++ b/SRC/clabrd.f
@@ -20,7 +20,7 @@
 *
 *  CLABRD reduces the first NB rows and columns of a complex general
 *  m by n matrix A to upper or lower real bidiagonal form by a unitary
-*  transformation Q' * A * P, and returns the matrices X and Y which
+*  transformation Q**H * A * P, and returns the matrices X and Y which
 *  are needed to apply the transformation to the unreduced part of A.
 *
 *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
@@ -101,7 +101,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors.
@@ -115,9 +115,9 @@
 *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  The elements of the vectors v and u together form the m-by-nb matrix
-*  V and the nb-by-n matrix U' which are needed, with X and Y, to apply
+*  V and the nb-by-n matrix U**H which are needed, with X and Y, to apply
 *  the transformation to the unreduced part of the matrix, using a block
-*  update of the form:  A := A - V*Y' - X*U'.
+*  update of the form:  A := A - V*Y**H - X*U**H.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with nb = 2:
diff --git a/SRC/claed7.f b/SRC/claed7.f
index 2f773a47..c8c34336 100644
--- a/SRC/claed7.f
+++ b/SRC/claed7.f
@@ -29,9 +29,9 @@
 *  eigenvalues and optionally eigenvectors of a dense or banded
 *  Hermitian matrix that has been reduced to tridiagonal form.
 *
-*    T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
+*    T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)
 *
-*    where Z = Q'u, u is a vector of length N with ones in the
+*    where Z = Q**Hu, u is a vector of length N with ones in the
 *    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
 *
 *     The eigenvectors of the original matrix are stored in Q, and the
diff --git a/SRC/claein.f b/SRC/claein.f
index b036e9e6..75b5c5ea 100644
--- a/SRC/claein.f
+++ b/SRC/claein.f
@@ -223,7 +223,7 @@
       DO 110 ITS = 1, N
 *
 *        Solve U*x = scale*v for a right eigenvector
-*          or U'*x = scale*v for a left eigenvector,
+*          or U**H *x = scale*v for a left eigenvector,
 *        overwriting x on v.
 *
          CALL CLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB, V,
diff --git a/SRC/clags2.f b/SRC/clags2.f
index 508d3ea7..4b035d3f 100644
--- a/SRC/clags2.f
+++ b/SRC/clags2.f
@@ -18,28 +18,26 @@
 *  CLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
 *  that if ( UPPER ) then
 *
-*            U'*A*Q = U'*( A1 A2 )*Q = ( x  0  )
-*                        ( 0  A3 )     ( x  x  )
+*            U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
+*                              ( 0  A3 )     ( x  x  )
 *  and
-*            V'*B*Q = V'*( B1 B2 )*Q = ( x  0  )
-*                        ( 0  B3 )     ( x  x  )
+*            V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
+*                             ( 0  B3 )     ( x  x  )
 *
 *  or if ( .NOT.UPPER ) then
 *
-*            U'*A*Q = U'*( A1 0  )*Q = ( x  x  )
-*                        ( A2 A3 )     ( 0  x  )
+*            U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
+*                              ( A2 A3 )     ( 0  x  )
 *  and
-*            V'*B*Q = V'*( B1 0  )*Q = ( x  x  )
-*                        ( B2 B3 )     ( 0  x  )
+*            V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
+*                              ( B2 B3 )     ( 0  x  )
 *  where
 *
-*    U = (     CSU      SNU ), V = (     CSV     SNV ),
-*        ( -CONJG(SNU)  CSU )      ( -CONJG(SNV) CSV )
+*    U = (   CSU    SNU ), V = (  CSV    SNV ),
+*        ( -SNU**H  CSU )      ( -SNV**H CSV )
 *
-*    Q = (     CSQ      SNQ )
-*        ( -CONJG(SNQ)  CSQ )
-*
-*  Z' denotes the conjugate transpose of Z.
+*    Q = (   CSQ    SNQ )
+*        ( -SNQ**H  CSQ )
 *
 *  The rows of the transformed A and B are parallel. Moreover, if the
 *  input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
@@ -135,8 +133,8 @@
          IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
      $        THEN
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+*           and (1,2) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA11R = CSL*A1
             UA12 = CSL*A2 + D1*SNL*A3
@@ -147,7 +145,7 @@
             AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 )
             AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 )
 *
-*           zero (1,2) elements of U'*A and V'*B
+*           zero (1,2) elements of U**H *A and V**H *B
 *
             IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN
                CALL CLARTG( -CMPLX( VB11R ), CONJG( VB12 ), CSQ, SNQ,
@@ -171,8 +169,8 @@
 *
          ELSE
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+*           and (2,2) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA21 = -CONJG( D1 )*SNL*A1
             UA22 = -CONJG( D1 )*SNL*A2 + CSL*A3
@@ -183,7 +181,7 @@
             AUA22 = ABS( SNL )*ABS1( A2 ) + ABS( CSL )*ABS( A3 )
             AVB22 = ABS( SNR )*ABS1( B2 ) + ABS( CSR )*ABS( B3 )
 *
-*           zero (2,2) elements of U'*A and V'*B, and then swap.
+*           zero (2,2) elements of U**H *A and V**H *B, and then swap.
 *
             IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN
                CALL CLARTG( -CONJG( VB21 ), CONJG( VB22 ), CSQ, SNQ, R )
@@ -232,8 +230,8 @@
          IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) )
      $        THEN
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+*           and (2,1) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA21 = -D1*SNR*A1 + CSR*A2
             UA22R = CSR*A3
@@ -244,7 +242,7 @@
             AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS1( A2 )
             AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS1( B2 )
 *
-*           zero (2,1) elements of U'*A and V'*B.
+*           zero (2,1) elements of U**H *A and V**H *B.
 *
             IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN
                CALL CLARTG( CMPLX( VB22R ), VB21, CSQ, SNQ, R )
@@ -264,8 +262,8 @@
 *
          ELSE
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+*           and (1,1) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA11 = CSR*A1 + CONJG( D1 )*SNR*A2
             UA12 = CONJG( D1 )*SNR*A3
@@ -276,7 +274,7 @@
             AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS1( A2 )
             AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS1( B2 )
 *
-*           zero (1,1) elements of U'*A and V'*B, and then swap.
+*           zero (1,1) elements of U**H *A and V**H *B, and then swap.
 *
             IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN
                CALL CLARTG( VB12, VB11, CSQ, SNQ, R )
diff --git a/SRC/clagtm.f b/SRC/clagtm.f
index 990f406a..c0cfae9b 100644
--- a/SRC/clagtm.f
+++ b/SRC/clagtm.f
@@ -189,7 +189,7 @@
   120       CONTINUE
          ELSE IF( LSAME( TRANS, 'T' ) ) THEN
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**T*X
 *
             DO 140 J = 1, NRHS
                IF( N.EQ.1 ) THEN
@@ -207,7 +207,7 @@
   140       CONTINUE
          ELSE IF( LSAME( TRANS, 'C' ) ) THEN
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**H*X
 *
             DO 160 J = 1, NRHS
                IF( N.EQ.1 ) THEN
diff --git a/SRC/clahef.f b/SRC/clahef.f
index 5527f202..3b30a2fc 100644
--- a/SRC/clahef.f
+++ b/SRC/clahef.f
@@ -21,15 +21,15 @@
 *  matrix A using the Bunch-Kaufman diagonal pivoting method. The
 *  partial factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
 *
-*  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) (  0  A22 ) (  0    I   )
+*  A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
+*        ( L21  I ) (  0  A22 ) (  0      I     )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
-*  Note that U' denotes the conjugate transpose of U.
+*  Note that U**H denotes the conjugate transpose of U.
 *
 *  CLAHEF is an auxiliary routine called by CHETRF. It uses blocked code
 *  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
@@ -344,7 +344,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**H = A11 - U12*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)
@@ -593,7 +593,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**H = A22 - L21*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)
diff --git a/SRC/clahr2.f b/SRC/clahr2.f
index ddf73b8b..9c002c2b 100644
--- a/SRC/clahr2.f
+++ b/SRC/clahr2.f
@@ -1,8 +1,9 @@
       SUBROUTINE CLAHR2( N, K, NB, A, LDA, TAU, T, LDT, Y, LDY )
 *
 *  -- LAPACK auxiliary routine (version 3.2.1)                        --
-*  -- LAPACK is a software package provided by Univ. of Tennessee,    --*  -- April 2009                                                      --
+*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*  -- April 2009                                                      --
 *
 *     .. Scalar Arguments ..
       INTEGER            K, LDA, LDT, LDY, N, NB
@@ -18,8 +19,8 @@
 *  CLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an unitary similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**H * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*v**H, and also the matrix Y = A * V * T.
 *
 *  This is an auxiliary routine called by CGEHRD.
 *
@@ -74,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -83,7 +84,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**H) * (A - Y*V**H).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -143,14 +144,14 @@
 *
 *           Update A(K+1:N,I)
 *
-*           Update I-th column of A - Y * V'
+*           Update I-th column of A - Y * V**H
 *
             CALL CLACGV( I-1, A( K+I-1, 1 ), LDA ) 
             CALL CGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
             CALL CLACGV( I-1, A( K+I-1, 1 ), LDA ) 
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T' * V**H to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -165,13 +166,13 @@
      $                  I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**H * b2
 *
             CALL CGEMV( 'Conjugate transpose', N-K-I+1, I-1, 
      $                  ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**H * w
 *
             CALL CTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', 
      $                  I-1, T, LDT,
diff --git a/SRC/clahrd.f b/SRC/clahrd.f
index f7b97b62..ffabde38 100644
--- a/SRC/clahrd.f
+++ b/SRC/clahrd.f
@@ -19,8 +19,8 @@
 *  CLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by a unitary similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**H * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
 *
 *  This is an OBSOLETE auxiliary routine. 
 *  This routine will be 'deprecated' in a  future release.
@@ -76,7 +76,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -85,7 +85,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**H) * (A - Y*V**H).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -132,14 +132,14 @@
 *
 *           Update A(1:n,i)
 *
-*           Compute i-th column of A - Y * V'
+*           Compute i-th column of A - Y * V**H
 *
             CALL CLACGV( I-1, A( K+I-1, 1 ), LDA )
             CALL CGEMV( 'No transpose', N, I-1, -ONE, Y, LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( 1, I ), 1 )
             CALL CLACGV( I-1, A( K+I-1, 1 ), LDA )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T**H * V**H to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -147,19 +147,19 @@
 *
 *           where V1 is unit lower triangular
 *
-*           w := V1' * b1
+*           w := V1**H * b1
 *
             CALL CCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
             CALL CTRMV( 'Lower', 'Conjugate transpose', 'Unit', I-1,
      $                  A( K+1, 1 ), LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**H *b2
 *
             CALL CGEMV( 'Conjugate transpose', N-K-I+1, I-1, ONE,
      $                  A( K+I, 1 ), LDA, A( K+I, I ), 1, ONE,
      $                  T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**H *w
 *
             CALL CTRMV( 'Upper', 'Conjugate transpose', 'Non-unit', I-1,
      $                  T, LDT, T( 1, NB ), 1 )
diff --git a/SRC/claic1.f b/SRC/claic1.f
index 37877d6c..f17c2b61 100644
--- a/SRC/claic1.f
+++ b/SRC/claic1.f
@@ -41,7 +41,7 @@
 *      diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
 *                                            [ conjg(gamma) ]
 *
-*  where  alpha =  conjg(x)'*w.
+*  where  alpha =  x**H*w.
 *
 *  Arguments
 *  =========
diff --git a/SRC/clalsd.f b/SRC/clalsd.f
index a670b0c1..da84ca19 100644
--- a/SRC/clalsd.f
+++ b/SRC/clalsd.f
@@ -243,7 +243,7 @@
          END IF
 *
 *        In the real version, B is passed to SLASDQ and multiplied
-*        internally by Q'. Here B is complex and that product is
+*        internally by Q**H. Here B is complex and that product is
 *        computed below in two steps (real and imaginary parts).
 *
          J = IRWB - 1
@@ -427,7 +427,7 @@
                END IF
 *
 *              In the real version, B is passed to SLASDQ and multiplied
-*              internally by Q'. Here B is complex and that product is
+*              internally by Q**H. Here B is complex and that product is
 *              computed below in two steps (real and imaginary parts).
 *
                J = IRWB - 1
diff --git a/SRC/claqhb.f b/SRC/claqhb.f
index 199a9028..c648dd2d 100644
--- a/SRC/claqhb.f
+++ b/SRC/claqhb.f
@@ -46,7 +46,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**H *U or A = L*L**H of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/claqp2.f b/SRC/claqp2.f
index a96fa28a..61ec1bfe 100644
--- a/SRC/claqp2.f
+++ b/SRC/claqp2.f
@@ -136,7 +136,7 @@
 *
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(offset+i:m,i+1:n) from the left.
+*           Apply H(i)**H to A(offset+i:m,i+1:n) from the left.
 *
             AII = A( OFFPI, I )
             A( OFFPI, I ) = CONE
diff --git a/SRC/claqps.f b/SRC/claqps.f
index acc4d472..ba4bf1c3 100644
--- a/SRC/claqps.f
+++ b/SRC/claqps.f
@@ -76,7 +76,7 @@
 *          Auxiliar vector.
 *
 *  F       (input/output) COMPLEX array, dimension (LDF,NB)
-*          Matrix F' = L*Y'*A.
+*          Matrix  F**H = L * Y**H * A.
 *
 *  LDF     (input) INTEGER
 *          The leading dimension of the array F. LDF >= max(1,N).
@@ -146,7 +146,7 @@
          END IF
 *
 *        Apply previous Householder reflectors to column K:
-*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
+*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H.
 *
          IF( K.GT.1 ) THEN
             DO 20 J = 1, K - 1
@@ -172,7 +172,7 @@
 *
 *        Compute Kth column of F:
 *
-*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
+*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K).
 *
          IF( K.LT.N ) THEN
             CALL CGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ),
@@ -187,7 +187,7 @@
    40    CONTINUE
 *
 *        Incremental updating of F:
-*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
+*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H
 *                    *A(RK:M,K).
 *
          IF( K.GT.1 ) THEN
@@ -200,7 +200,7 @@
          END IF
 *
 *        Update the current row of A:
-*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
+*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H.
 *
          IF( K.LT.N ) THEN
             CALL CGEMM( 'No transpose', 'Conjugate transpose', 1, N-K,
@@ -241,7 +241,7 @@
 *
 *     Apply the block reflector to the rest of the matrix:
 *     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
-*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
+*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H.
 *
       IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
          CALL CGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB,
diff --git a/SRC/claqsb.f b/SRC/claqsb.f
index bcd97d62..8ea7adff 100644
--- a/SRC/claqsb.f
+++ b/SRC/claqsb.f
@@ -46,7 +46,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T *U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/clar1v.f b/SRC/clar1v.f
index f27e46f3..9fff18c0 100644
--- a/SRC/clar1v.f
+++ b/SRC/clar1v.f
@@ -25,14 +25,14 @@
 *
 *  CLAR1V computes the (scaled) r-th column of the inverse of
 *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix
-*  L D L^T - sigma I. When sigma is close to an eigenvalue, the
+*  L D L**T - sigma I. When sigma is close to an eigenvalue, the
 *  computed vector is an accurate eigenvector. Usually, r corresponds
 *  to the index where the eigenvector is largest in magnitude.
 *  The following steps accomplish this computation :
-*  (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T,
-*  (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T,
+*  (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
+*  (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
 *  (c) Computation of the diagonal elements of the inverse of
-*      L D L^T - sigma I by combining the above transforms, and choosing
+*      L D L**T - sigma I by combining the above transforms, and choosing
 *      r as the index where the diagonal of the inverse is (one of the)
 *      largest in magnitude.
 *  (d) Computation of the (scaled) r-th column of the inverse using the
@@ -43,40 +43,40 @@
 *  =========
 *
 *  N        (input) INTEGER
-*           The order of the matrix L D L^T.
+*           The order of the matrix L D L**T.
 *
 *  B1       (input) INTEGER
-*           First index of the submatrix of L D L^T.
+*           First index of the submatrix of L D L**T.
 *
 *  BN       (input) INTEGER
-*           Last index of the submatrix of L D L^T.
+*           Last index of the submatrix of L D L**T.
 *
-*  LAMBDA    (input) REAL            
+*  LAMBDA    (input) REAL
 *           The shift. In order to compute an accurate eigenvector,
 *           LAMBDA should be a good approximation to an eigenvalue
-*           of L D L^T.
+*           of L D L**T.
 *
-*  L        (input) REAL             array, dimension (N-1)
+*  L        (input) REAL array, dimension (N-1)
 *           The (n-1) subdiagonal elements of the unit bidiagonal matrix
 *           L, in elements 1 to N-1.
 *
-*  D        (input) REAL             array, dimension (N)
+*  D        (input) REAL array, dimension (N)
 *           The n diagonal elements of the diagonal matrix D.
 *
-*  LD       (input) REAL             array, dimension (N-1)
+*  LD       (input) REAL array, dimension (N-1)
 *           The n-1 elements L(i)*D(i).
 *
-*  LLD      (input) REAL             array, dimension (N-1)
+*  LLD      (input) REAL array, dimension (N-1)
 *           The n-1 elements L(i)*L(i)*D(i).
 *
-*  PIVMIN   (input) REAL            
+*  PIVMIN   (input) REAL
 *           The minimum pivot in the Sturm sequence.
 *
-*  GAPTOL   (input) REAL            
+*  GAPTOL   (input) REAL
 *           Tolerance that indicates when eigenvector entries are negligible
 *           w.r.t. their contribution to the residual.
 *
-*  Z        (input/output) COMPLEX          array, dimension (N)
+*  Z        (input/output) COMPLEX array, dimension (N)
 *           On input, all entries of Z must be set to 0.
 *           On output, Z contains the (scaled) r-th column of the
 *           inverse. The scaling is such that Z(R) equals 1.
@@ -86,20 +86,20 @@
 *
 *  NEGCNT   (output) INTEGER
 *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
-*           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.
+*           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.
 *
-*  ZTZ      (output) REAL            
+*  ZTZ      (output) REAL
 *           The square of the 2-norm of Z.
 *
-*  MINGMA   (output) REAL            
+*  MINGMA   (output) REAL
 *           The reciprocal of the largest (in magnitude) diagonal
-*           element of the inverse of L D L^T - sigma I.
+*           element of the inverse of L D L**T - sigma I.
 *
 *  R        (input/output) INTEGER
 *           The twist index for the twisted factorization used to
 *           compute Z.
 *           On input, 0 <= R <= N. If R is input as 0, R is set to
-*           the index where (L D L^T - sigma I)^{-1} is largest
+*           the index where (L D L**T - sigma I)^{-1} is largest
 *           in magnitude. If 1 <= R <= N, R is unchanged.
 *           On output, R contains the twist index used to compute Z.
 *           Ideally, R designates the position of the maximum entry in the
@@ -109,18 +109,18 @@
 *           The support of the vector in Z, i.e., the vector Z is
 *           nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ).
 *
-*  NRMINV   (output) REAL            
+*  NRMINV   (output) REAL
 *           NRMINV = 1/SQRT( ZTZ )
 *
-*  RESID    (output) REAL            
+*  RESID    (output) REAL
 *           The residual of the FP vector.
 *           RESID = ABS( MINGMA )/SQRT( ZTZ )
 *
-*  RQCORR   (output) REAL            
+*  RQCORR   (output) REAL
 *           The Rayleigh Quotient correction to LAMBDA.
 *           RQCORR = MINGMA*TMP
 *
-*  WORK     (workspace) REAL             array, dimension (4*N)
+*  WORK     (workspace) REAL array, dimension (4*N)
 *
 *  Further Details
 *  ===============
diff --git a/SRC/clarf.f b/SRC/clarf.f
index e4ee75ca..c9fd3ef0 100644
--- a/SRC/clarf.f
+++ b/SRC/clarf.f
@@ -22,13 +22,13 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
 *  If tau = 0, then H is taken to be the unit matrix.
 *
-*  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
+*  To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
 *  tau.
 *
 *  Arguments
@@ -126,12 +126,12 @@
 *
          IF( LASTV.GT.0 ) THEN
 *
-*           w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)
+*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
 *
             CALL CGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
      $           C, LDC, V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'
+*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
 *
             CALL CGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
          END IF
@@ -146,7 +146,7 @@
             CALL CGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
      $           V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'
+*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
 *
             CALL CGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
          END IF
diff --git a/SRC/clarfb.f b/SRC/clarfb.f
index 9fd89d67..c4980bd0 100644
--- a/SRC/clarfb.f
+++ b/SRC/clarfb.f
@@ -19,19 +19,19 @@
 *  Purpose
 *  =======
 *
-*  CLARFB applies a complex block reflector H or its transpose H' to a
+*  CLARFB applies a complex block reflector H or its transpose H**H to a
 *  complex M-by-N matrix C, from either the left or the right.
 *
 *  Arguments
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**H from the Left
+*          = 'R': apply H or H**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Conjugate transpose)
+*          = 'C': apply H**H (Conjugate transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -76,7 +76,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -157,13 +157,13 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILACLR( M, K, V, LDV ) )
                LASTC = ILACLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
 *              W := C1'
 *
@@ -178,35 +178,35 @@
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2
+*                 W := W + C2**H *V2
 *
                   CALL CGEMM( 'Conjugate transpose', 'No transpose',
      $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,
      $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**H
 *
                IF( M.GT.K ) THEN
 *
-*                 C2 := C2 - V2 * W'
+*                 C2 := C2 - V2 * W**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTV-K, LASTC, K, -ONE, V( K+1, 1 ), LDV,
      $                 WORK, LDWORK, ONE, C( K+1, 1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**H
 *
                DO 30 J = 1, K
                   DO 20 I = 1, LASTC
@@ -216,7 +216,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILACLR( N, K, V, LDV ) )
                LASTC = ILACLR( M, LASTV, C, LDC )
@@ -243,16 +243,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - W * V2'
+*                 C2 := C2 - W * V2**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, LASTV-K, K,
@@ -260,7 +260,7 @@
      $                 ONE, C( 1, K+1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
@@ -282,15 +282,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILACLR( M, K, V, LDV ) )
                LASTC = ILACLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
-*              W := C2'
+*              W := C2**H
 *
                DO 70 J = 1, K
                   CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -305,36 +305,36 @@
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1
+*                 W := W + C1**H*V1
 *
                   CALL CGEMM( 'Conjugate transpose', 'No transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1 * W'
+*                 C1 := C1 - V1 * W**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**H
 *
                DO 90 J = 1, K
                   DO 80 I = 1, LASTC
@@ -345,7 +345,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILACLR( N, K, V, LDV ) )
                LASTC = ILACLR( M, LASTV, C, LDC )
@@ -373,23 +373,23 @@
      $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - W * V1'
+*                 C1 := C1 - W * V1**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
@@ -415,28 +415,28 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILACLC( K, M, V, LDV ) )
                LASTC = ILACLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
-*              W := C1'
+*              W := C1**H
 *
                DO 130 J = 1, K
                   CALL CCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
                   CALL CLACGV( LASTC, WORK( 1, J ), 1 )
   130          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2'
+*                 W := W + C2**H*V2**H
 *
                   CALL CGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTC, K, LASTV-K,
@@ -444,16 +444,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL CTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**H * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2' * W'
+*                 C2 := C2 - V2**H * W**H
 *
                   CALL CGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTV-K, LASTC, K,
@@ -466,7 +466,7 @@
                CALL CTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**H
 *
                DO 150 J = 1, K
                   DO 140 I = 1, LASTC
@@ -476,12 +476,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILACLC( K, N, V, LDV ) )
                LASTC = ILACLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C1
 *
@@ -489,20 +489,20 @@
                   CALL CCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL CTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2 * V2'
+*                 W := W + C2 * V2**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
      $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL CTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -541,15 +541,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILACLC( K, M, V, LDV ) )
                LASTC = ILACLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
-*              W := C2'
+*              W := C2**H
 *
                DO 190 J = 1, K
                   CALL CCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -557,30 +557,30 @@
                   CALL CLACGV( LASTC, WORK( 1, J ), 1 )
   190          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1'
+*                 W := W + C1**H * V1**H
 *
                   CALL CGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTC, K, LASTV-K,
      $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**H * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1' * W'
+*                 C1 := C1 - V1**H * W**H
 *
                   CALL CGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTV-K, LASTC, K,
@@ -593,7 +593,7 @@
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**H
 *
                DO 210 J = 1, K
                   DO 200 I = 1, LASTC
@@ -604,12 +604,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILACLC( K, N, V, LDV ) )
                LASTC = ILACLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C2
 *
@@ -618,21 +618,21 @@
      $                 WORK( 1, J ), 1 )
   220          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL CTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1 * V1'
+*                 W := W + C1 * V1**H
 *
                   CALL CGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,
      $                 WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
diff --git a/SRC/clarfg.f b/SRC/clarfg.f
index 786419c0..274b8993 100644
--- a/SRC/clarfg.f
+++ b/SRC/clarfg.f
@@ -19,13 +19,13 @@
 *  CLARFG generates a complex elementary reflector H of order n, such
 *  that
 *
-*        H' * ( alpha ) = ( beta ),   H' * H = I.
-*             (   x   )   (   0  )
+*        H**H * ( alpha ) = ( beta ),   H**H * H = I.
+*               (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, with beta real, and x is an
 *  (n-1)-element complex vector. H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**H ) ,
 *                      ( v )
 *
 *  where tau is a complex scalar and v is a complex (n-1)-element
diff --git a/SRC/clarfgp.f b/SRC/clarfgp.f
index 35b8a651..0e189ab1 100644
--- a/SRC/clarfgp.f
+++ b/SRC/clarfgp.f
@@ -19,13 +19,13 @@
 *  CLARFGP generates a complex elementary reflector H of order n, such
 *  that
 *
-*        H' * ( alpha ) = ( beta ),   H' * H = I.
-*             (   x   )   (   0  )
+*        H**H * ( alpha ) = ( beta ),   H**H * H = I.
+*               (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, beta is real and non-negative, and
 *  x is an (n-1)-element complex vector.  H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**H ) ,
 *                      ( v )
 *
 *  where tau is a complex scalar and v is a complex (n-1)-element
diff --git a/SRC/clarft.f b/SRC/clarft.f
index 3b8b9976..d4eff11f 100644
--- a/SRC/clarft.f
+++ b/SRC/clarft.f
@@ -26,12 +26,12 @@
 *  If STOREV = 'C', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th column of the array V, and
 *
-*     H  =  I - V * T * V'
+*     H  =  I - V * T * V**H
 *
 *  If STOREV = 'R', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th row of the array V, and
 *
-*     H  =  I - V' * T * V
+*     H  =  I - V**H * T * V
 *
 *  Arguments
 *  =========
@@ -150,7 +150,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i)
+*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)
 *
                   CALL CGEMV( 'Conjugate transpose', J-I+1, I-1,
      $                        -TAU( I ), V( I, 1 ), LDV, V( I, I ), 1,
@@ -162,7 +162,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)'
+*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H
 *
                   IF( I.LT.J )
      $               CALL CLACGV( J-I, V( I, I+1 ), LDV )
@@ -211,7 +211,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i)
+*                            - tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)
 *
                      CALL CGEMV( 'Conjugate transpose', N-K+I-J+1, K-I,
      $                           -TAU( I ), V( J, I+1 ), LDV, V( J, I ),
@@ -227,7 +227,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)'
+*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H
 *
                      CALL CLACGV( N-K+I-1-J+1, V( I, J ), LDV )
                      CALL CGEMV( 'No transpose', K-I, N-K+I-J+1,
diff --git a/SRC/clarfx.f b/SRC/clarfx.f
index 5b76e6e3..97e14f1c 100644
--- a/SRC/clarfx.f
+++ b/SRC/clarfx.f
@@ -22,7 +22,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
diff --git a/SRC/clarrv.f b/SRC/clarrv.f
index 42d7d9aa..234fb209 100644
--- a/SRC/clarrv.f
+++ b/SRC/clarrv.f
@@ -25,7 +25,7 @@
 *  =======
 *
 *  CLARRV computes the eigenvectors of the tridiagonal matrix
-*  T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T.
+*  T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
 *  The input eigenvalues should have been computed by SLARRE.
 *
 *  Arguments
diff --git a/SRC/clarz.f b/SRC/clarz.f
index ead41fe0..33277039 100644
--- a/SRC/clarz.f
+++ b/SRC/clarz.f
@@ -21,13 +21,13 @@
 *  M-by-N matrix C, from either the left or the right. H is represented
 *  in the form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
 *  If tau = 0, then H is taken to be the unit matrix.
 *
-*  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
+*  To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
 *  tau.
 *
 *  H is a product of k elementary reflectors as returned by CTZRZF.
@@ -105,7 +105,7 @@
             CALL CCOPY( N, C, LDC, WORK, 1 )
             CALL CLACGV( N, WORK, 1 )
 *
-*           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) )
+*           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
 *
             CALL CGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
      $                  LDC, V, INCV, ONE, WORK, 1 )
@@ -116,7 +116,7 @@
             CALL CAXPY( N, -TAU, WORK, 1, C, LDC )
 *
 *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                               tau * v( 1:l ) * conjg( w( 1:n )' )
+*                               tau * v( 1:l ) * w( 1:n )**H
 *
             CALL CGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
      $                  LDC )
@@ -142,7 +142,7 @@
             CALL CAXPY( M, -TAU, WORK, 1, C, 1 )
 *
 *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
-*                               tau * w( 1:m ) * v( 1:l )'
+*                               tau * w( 1:m ) * v( 1:l )**H
 *
             CALL CGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
      $                  LDC )
diff --git a/SRC/clarzb.f b/SRC/clarzb.f
index 82a46c7d..099f846f 100644
--- a/SRC/clarzb.f
+++ b/SRC/clarzb.f
@@ -27,12 +27,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**H from the Left
+*          = 'R': apply H or H**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Conjugate transpose)
+*          = 'C': apply H**H (Conjugate transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -77,7 +77,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -140,28 +140,28 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        Form  H * C  or  H' * C
+*        Form  H * C  or  H**H * C
 *
-*        W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
+*        W( 1:n, 1:k ) = C( 1:k, 1:n )**H
 *
          DO 10 J = 1, K
             CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10    CONTINUE
 *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
-*                        conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
+*                        C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL CGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
      $                  ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
      $                  LDWORK )
 *
-*        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T'  or  W( 1:m, 1:k ) * T
+*        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T  or  W( 1:m, 1:k ) * T
 *
          CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
      $               LDT, WORK, LDWORK )
 *
-*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
+*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
 *
          DO 30 J = 1, N
             DO 20 I = 1, K
@@ -170,7 +170,7 @@
    30    CONTINUE
 *
 *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                    conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
+*                            V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
 *
          IF( L.GT.0 )
      $      CALL CGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
@@ -178,7 +178,7 @@
 *
       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*        Form  C * H  or  C * H'
+*        Form  C * H  or  C * H**H
 *
 *        W( 1:m, 1:k ) = C( 1:m, 1:k )
 *
@@ -187,14 +187,14 @@
    40    CONTINUE
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
-*                        C( 1:m, n-l+1:n ) * conjg( V( 1:k, 1:l )' )
+*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
 *
          IF( L.GT.0 )
      $      CALL CGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
      $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T )  or
-*                        W( 1:m, 1:k ) * conjg( T' )
+*                        W( 1:m, 1:k ) * T**H
 *
          DO 50 J = 1, K
             CALL CLACGV( K-J+1, T( J, J ), 1 )
diff --git a/SRC/clarzt.f b/SRC/clarzt.f
index 8d807ab3..3abd29b0 100644
--- a/SRC/clarzt.f
+++ b/SRC/clarzt.f
@@ -164,7 +164,7 @@
 *
             IF( I.LT.K ) THEN
 *
-*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
+*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**H
 *
                CALL CLACGV( N, V( I, 1 ), LDV )
                CALL CGEMV( 'No transpose', K-I, N, -TAU( I ),
diff --git a/SRC/clasyf.f b/SRC/clasyf.f
index 136ef5e6..ea749f72 100644
--- a/SRC/clasyf.f
+++ b/SRC/clasyf.f
@@ -21,15 +21,15 @@
 *  A using the Bunch-Kaufman diagonal pivoting method. The partial
 *  factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
 *
-*  A  =  ( L11  0 ) ( D    0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) ( 0   A22 ) (  0    I   )
+*  A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
+*        ( L21  I ) ( 0   A22 ) (  0       I    )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
-*  Note that U' denotes the transpose of U.
+*  Note that U**T denotes the transpose of U.
 *
 *  CLASYF is an auxiliary routine called by CSYTRF. It uses blocked code
 *  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
@@ -322,7 +322,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
 *
 *        computing blocks of NB columns at a time
 *
@@ -546,7 +546,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
 *
 *        computing blocks of NB columns at a time
 *
diff --git a/SRC/clatrd.f b/SRC/clatrd.f
index 24b3ba40..6d736a39 100644
--- a/SRC/clatrd.f
+++ b/SRC/clatrd.f
@@ -19,7 +19,7 @@
 *
 *  CLATRD reduces NB rows and columns of a complex Hermitian matrix A to
 *  Hermitian tridiagonal form by a unitary similarity
-*  transformation Q' * A * Q, and returns the matrices V and W which are
+*  transformation Q**H * A * Q, and returns the matrices V and W which are
 *  needed to apply the transformation to the unreduced part of A.
 *
 *  If UPLO = 'U', CLATRD reduces the last NB rows and columns of a
@@ -96,7 +96,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
@@ -109,7 +109,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -118,7 +118,7 @@
 *  The elements of the vectors v together form the n-by-nb matrix V
 *  which is needed, with W, to apply the transformation to the unreduced
 *  part of the matrix, using a Hermitian rank-2k update of the form:
-*  A := A - V*W' - W*V'.
+*  A := A - V*W**H - W*V**H.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with n = 5 and nb = 2:
diff --git a/SRC/clatrz.f b/SRC/clatrz.f
index 048892b8..a572b8ce 100644
--- a/SRC/clatrz.f
+++ b/SRC/clatrz.f
@@ -64,7 +64,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/clatzm.f b/SRC/clatzm.f
index 87ec6835..ed410441 100644
--- a/SRC/clatzm.f
+++ b/SRC/clatzm.f
@@ -21,8 +21,8 @@
 *
 *  CLATZM applies a Householder matrix generated by CTZRQF to a matrix.
 *
-*  Let P = I - tau*u*u',   u = ( 1 ),
-*                              ( v )
+*  Let P = I - tau*u*u**H,   u = ( 1 ),
+*                                ( v )
 *  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
 *  SIDE = 'R'.
 *
@@ -112,14 +112,14 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        w :=  conjg( C1 + v' * C2 )
+*        w :=  ( C1 + v**H * C2 )**H
 *
          CALL CCOPY( N, C1, LDC, WORK, 1 )
          CALL CLACGV( N, WORK, 1 )
          CALL CGEMV( 'Conjugate transpose', M-1, N, ONE, C2, LDC, V,
      $               INCV, ONE, WORK, 1 )
 *
-*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
+*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
 *        [ C2 ]    [ C2 ]        [ v ]
 *
          CALL CLACGV( N, WORK, 1 )
@@ -134,7 +134,7 @@
          CALL CGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
+*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
 *
          CALL CAXPY( M, -TAU, WORK, 1, C1, 1 )
          CALL CGERC( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
diff --git a/SRC/clauu2.f b/SRC/clauu2.f
index ccfecec9..732f420b 100644
--- a/SRC/clauu2.f
+++ b/SRC/clauu2.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  CLAUU2 computes the product U * U' or L' * L, where the triangular
+*  CLAUU2 computes the product U * U**H or L**H * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) COMPLEX array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**H;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**H * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -100,7 +100,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product U * U'.
+*        Compute the product U * U**H.
 *
          DO 10 I = 1, N
             AII = A( I, I )
@@ -119,7 +119,7 @@
 *
       ELSE
 *
-*        Compute the product L' * L.
+*        Compute the product L**H * L.
 *
          DO 20 I = 1, N
             AII = A( I, I )
diff --git a/SRC/clauum.f b/SRC/clauum.f
index 498ae80a..01e5d4c6 100644
--- a/SRC/clauum.f
+++ b/SRC/clauum.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  CLAUUM computes the product U * U' or L' * L, where the triangular
+*  CLAUUM computes the product U * U**H or L**H * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) COMPLEX array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**H;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**H * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -114,7 +114,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the product U * U'.
+*           Compute the product U * U**H.
 *
             DO 10 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
@@ -134,7 +134,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute the product L' * L.
+*           Compute the product L**H * L.
 *
             DO 20 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
diff --git a/SRC/cpbcon.f b/SRC/cpbcon.f
index a3f4a891..cb2238aa 100644
--- a/SRC/cpbcon.f
+++ b/SRC/cpbcon.f
@@ -147,7 +147,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK,
@@ -166,7 +166,7 @@
      $                   KD, AB, LDAB, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL CLATBS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK,
diff --git a/SRC/cpbsv.f b/SRC/cpbsv.f
index e14b5d9f..9b23f182 100644
--- a/SRC/cpbsv.f
+++ b/SRC/cpbsv.f
@@ -135,7 +135,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H*U or A = L*L**H.
 *
       CALL CPBTRF( UPLO, N, KD, AB, LDAB, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/cpbsvx.f b/SRC/cpbsvx.f
index 9407a07e..cea2d80b 100644
--- a/SRC/cpbsvx.f
+++ b/SRC/cpbsvx.f
@@ -351,7 +351,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
          IF( UPPER ) THEN
             DO 40 J = 1, N
diff --git a/SRC/cpbtf2.f b/SRC/cpbtf2.f
index 4a6bb91e..62547f9a 100644
--- a/SRC/cpbtf2.f
+++ b/SRC/cpbtf2.f
@@ -20,9 +20,9 @@
 *  positive definite band matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
-*  where U is an upper triangular matrix, U' is the conjugate transpose
+*     A = U**H * U ,  if UPLO = 'U', or
+*     A = L  * L**H,  if UPLO = 'L',
+*  where U is an upper triangular matrix, U**H is the conjugate transpose
 *  of U, and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -52,7 +52,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**H *U or A = L*L**H of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
@@ -137,7 +137,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H * U.
 *
          DO 10 J = 1, N
 *
@@ -165,7 +165,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**H.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/cpbtrs.f b/SRC/cpbtrs.f
index 6db8cd7b..857e1281 100644
--- a/SRC/cpbtrs.f
+++ b/SRC/cpbtrs.f
@@ -107,11 +107,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H *U.
 *
          DO 10 J = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**H *X = B, overwriting B with X.
 *
             CALL CTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
      $                  KD, AB, LDAB, B( 1, J ), 1 )
@@ -123,7 +123,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**H.
 *
          DO 20 J = 1, NRHS
 *
@@ -132,7 +132,7 @@
             CALL CTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
 *
-*           Solve L'*X = B, overwriting B with X.
+*           Solve L**H *X = B, overwriting B with X.
 *
             CALL CTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
      $                  KD, AB, LDAB, B( 1, J ), 1 )
diff --git a/SRC/cpocon.f b/SRC/cpocon.f
index 9faf372d..526e4410 100644
--- a/SRC/cpocon.f
+++ b/SRC/cpocon.f
@@ -136,7 +136,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
@@ -154,7 +154,7 @@
      $                   A, LDA, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL CLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
diff --git a/SRC/cposv.f b/SRC/cposv.f
index a37afc63..1520561a 100644
--- a/SRC/cposv.f
+++ b/SRC/cposv.f
@@ -105,7 +105,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H*U or A = L*L**H.
 *
       CALL CPOTRF( UPLO, N, A, LDA, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/cposvx.f b/SRC/cposvx.f
index 61563158..b829faf2 100644
--- a/SRC/cposvx.f
+++ b/SRC/cposvx.f
@@ -319,7 +319,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
          CALL CLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL CPOTRF( UPLO, N, AF, LDAF, INFO )
diff --git a/SRC/cpotf2.f b/SRC/cpotf2.f
index f15d8d04..49d31d89 100644
--- a/SRC/cpotf2.f
+++ b/SRC/cpotf2.f
@@ -20,8 +20,8 @@
 *  positive definite matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
+*     A = U**H * U ,  if UPLO = 'U', or
+*     A = L  * L**H,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -48,7 +48,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U'*U  or A = L*L'.
+*          factorization A = U**H *U  or A = L*L**H.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -109,7 +109,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H *U.
 *
          DO 10 J = 1, N
 *
@@ -136,7 +136,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**H.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/cpotrf.f b/SRC/cpotrf.f
index 34f45412..174e582c 100644
--- a/SRC/cpotrf.f
+++ b/SRC/cpotrf.f
@@ -117,7 +117,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the Cholesky factorization A = U'*U.
+*           Compute the Cholesky factorization A = U**H *U.
 *
             DO 10 J = 1, N, NB
 *
@@ -146,7 +146,7 @@
 *
          ELSE
 *
-*           Compute the Cholesky factorization A = L*L'.
+*           Compute the Cholesky factorization A = L*L**H.
 *
             DO 20 J = 1, N, NB
 *
diff --git a/SRC/cpotri.f b/SRC/cpotri.f
index 041b0802..1d8ff3b7 100644
--- a/SRC/cpotri.f
+++ b/SRC/cpotri.f
@@ -86,7 +86,7 @@
       IF( INFO.GT.0 )
      $   RETURN
 *
-*     Form inv(U)*inv(U)' or inv(L)'*inv(L).
+*     Form inv(U) * inv(U)**H or inv(L)**H * inv(L).
 *
       CALL CLAUUM( UPLO, N, A, LDA, INFO )
 *
diff --git a/SRC/cpotrs.f b/SRC/cpotrs.f
index 6020d33d..fe5e8300 100644
--- a/SRC/cpotrs.f
+++ b/SRC/cpotrs.f
@@ -100,9 +100,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H *U.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**H *X = B, overwriting B with X.
 *
          CALL CTRSM( 'Left', 'Upper', 'Conjugate transpose', 'Non-unit',
      $               N, NRHS, ONE, A, LDA, B, LDB )
@@ -113,14 +113,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**H.
 *
 *        Solve L*X = B, overwriting B with X.
 *
          CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
      $               NRHS, ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**H *X = B, overwriting B with X.
 *
          CALL CTRSM( 'Left', 'Lower', 'Conjugate transpose', 'Non-unit',
      $               N, NRHS, ONE, A, LDA, B, LDB )
diff --git a/SRC/cppcon.f b/SRC/cppcon.f
index 10ff4772..7b67efc0 100644
--- a/SRC/cppcon.f
+++ b/SRC/cppcon.f
@@ -135,7 +135,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL CLATPS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, AP, WORK, SCALEL, RWORK, INFO )
@@ -153,7 +153,7 @@
      $                   AP, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL CLATPS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, AP, WORK, SCALEU, RWORK, INFO )
diff --git a/SRC/cppsv.f b/SRC/cppsv.f
index 0e437b73..f697442f 100644
--- a/SRC/cppsv.f
+++ b/SRC/cppsv.f
@@ -22,7 +22,7 @@
 *  packed format and X and B are N-by-NRHS matrices.
 *
 *  The Cholesky decomposition is used to factor A as
-*     A = U**H* U,  if UPLO = 'U', or
+*     A = U**H * U,  if UPLO = 'U', or
 *     A = L * L**H,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is a lower triangular
 *  matrix.  The factored form of A is then used to solve the system of
@@ -49,7 +49,7 @@
 *          is stored in the array AP as follows:
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
 *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
-*          See below for further details.  
+*          See below for further details.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
 *          factorization A = U**H*U or A = L*L**H, in the same storage
@@ -117,7 +117,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
       CALL CPPTRF( UPLO, N, AP, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/cppsvx.f b/SRC/cppsvx.f
index 43522997..0997cdef 100644
--- a/SRC/cppsvx.f
+++ b/SRC/cppsvx.f
@@ -43,8 +43,8 @@
 *
 *  2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
 *     factor the matrix A (after equilibration if FACT = 'E') as
-*        A = U'* U ,  if UPLO = 'U', or
-*        A = L * L',  if UPLO = 'L',
+*        A = U**H * U ,  if UPLO = 'U', or
+*        A = L * L**H,  if UPLO = 'L',
 *     where U is an upper triangular matrix, L is a lower triangular
 *     matrix, and ' indicates conjugate transpose.
 *
@@ -117,7 +117,7 @@
 *
 *          If FACT = 'N', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the original
+*          factorization A = U**H * U or A = L * L**H of the original
 *          matrix A.
 *
 *          If FACT = 'E', then AFP is an output argument and on exit
@@ -324,7 +324,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H * U or A = L * L**H.
 *
          CALL CCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL CPPTRF( UPLO, N, AFP, INFO )
diff --git a/SRC/cpptrf.f b/SRC/cpptrf.f
index bf214eb7..d3080090 100644
--- a/SRC/cpptrf.f
+++ b/SRC/cpptrf.f
@@ -115,7 +115,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H * U.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -140,7 +140,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L * L**H.
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/cpptri.f b/SRC/cpptri.f
index bcab4542..753331a9 100644
--- a/SRC/cpptri.f
+++ b/SRC/cpptri.f
@@ -97,7 +97,7 @@
      $   RETURN
       IF( UPPER ) THEN
 *
-*        Compute the product inv(U) * inv(U)'.
+*        Compute the product inv(U) * inv(U)**H.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -111,7 +111,7 @@
 *
       ELSE
 *
-*        Compute the product inv(L)' * inv(L).
+*        Compute the product inv(L)**H * inv(L).
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/cpptrs.f b/SRC/cpptrs.f
index f9d2c2fd..dc06efaf 100644
--- a/SRC/cpptrs.f
+++ b/SRC/cpptrs.f
@@ -96,11 +96,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H * U.
 *
          DO 10 I = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**H *X = B, overwriting B with X.
 *
             CALL CTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
      $                  AP, B( 1, I ), 1 )
@@ -112,7 +112,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L * L**H.
 *
          DO 20 I = 1, NRHS
 *
@@ -121,7 +121,7 @@
             CALL CTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
 *
-*           Solve L'*X = Y, overwriting B with X.
+*           Solve L**H *X = Y, overwriting B with X.
 *
             CALL CTPSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
      $                  AP, B( 1, I ), 1 )
diff --git a/SRC/cptcon.f b/SRC/cptcon.f
index 6ed1103f..e60b41b2 100644
--- a/SRC/cptcon.f
+++ b/SRC/cptcon.f
@@ -118,7 +118,7 @@
 *        m(i,j) =  abs(A(i,j)), i = j,
 *        m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**H.
 *
 *     Solve M(L) * x = e.
 *
@@ -127,7 +127,7 @@
          RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )
    20 CONTINUE
 *
-*     Solve D * M(L)' * x = b.
+*     Solve D * M(L)**H * x = b.
 *
       RWORK( N ) = RWORK( N ) / D( N )
       DO 30 I = N - 1, 1, -1
diff --git a/SRC/cptrfs.f b/SRC/cptrfs.f
index 0e4e9dd3..88e64504 100644
--- a/SRC/cptrfs.f
+++ b/SRC/cptrfs.f
@@ -327,7 +327,7 @@
 *           m(i,j) =  abs(A(i,j)), i = j,
 *           m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**H.
 *
 *        Solve M(L) * x = e.
 *
@@ -336,7 +336,7 @@
             RWORK( I ) = ONE + RWORK( I-1 )*ABS( EF( I-1 ) )
    70    CONTINUE
 *
-*        Solve D * M(L)' * x = b.
+*        Solve D * M(L)**H * x = b.
 *
          RWORK( N ) = RWORK( N ) / DF( N )
          DO 80 I = N - 1, 1, -1
diff --git a/SRC/cptsv.f b/SRC/cptsv.f
index 98032219..bd263cc4 100644
--- a/SRC/cptsv.f
+++ b/SRC/cptsv.f
@@ -85,7 +85,7 @@
          RETURN
       END IF
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**H (or U**H*D*U) factorization of A.
 *
       CALL CPTTRF( N, D, E, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/cptsvx.f b/SRC/cptsvx.f
index 23361c70..6b98480d 100644
--- a/SRC/cptsvx.f
+++ b/SRC/cptsvx.f
@@ -191,7 +191,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the L*D*L' (or U'*D*U) factorization of A.
+*        Compute the L*D*L**H (or U**H*D*U) factorization of A.
 *
          CALL SCOPY( N, D, 1, DF, 1 )
          IF( N.GT.1 )
diff --git a/SRC/cpttrf.f b/SRC/cpttrf.f
index d3509013..91d20d36 100644
--- a/SRC/cpttrf.f
+++ b/SRC/cpttrf.f
@@ -16,9 +16,9 @@
 *  Purpose
 *  =======
 *
-*  CPTTRF computes the L*D*L' factorization of a complex Hermitian
+*  CPTTRF computes the L*D*L**H factorization of a complex Hermitian
 *  positive definite tridiagonal matrix A.  The factorization may also
-*  be regarded as having the form A = U'*D*U.
+*  be regarded as having the form A = U**H *D*U.
 *
 *  Arguments
 *  =========
@@ -29,14 +29,14 @@
 *  D       (input/output) REAL array, dimension (N)
 *          On entry, the n diagonal elements of the tridiagonal matrix
 *          A.  On exit, the n diagonal elements of the diagonal matrix
-*          D from the L*D*L' factorization of A.
+*          D from the L*D*L**H factorization of A.
 *
 *  E       (input/output) COMPLEX array, dimension (N-1)
 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
 *          matrix A.  On exit, the (n-1) subdiagonal elements of the
-*          unit bidiagonal factor L from the L*D*L' factorization of A.
+*          unit bidiagonal factor L from the L*D*L**H factorization of A.
 *          E can also be regarded as the superdiagonal of the unit
-*          bidiagonal factor U from the U'*D*U factorization of A.
+*          bidiagonal factor U from the U**H *D*U factorization of A.
 *
 *  INFO    (output) INTEGER
 *          = 0: successful exit
@@ -78,7 +78,7 @@
       IF( N.EQ.0 )
      $   RETURN
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**H (or U**H *D*U) factorization of A.
 *
       I4 = MOD( N-1, 4 )
       DO 10 I = 1, I4
diff --git a/SRC/cpttrs.f b/SRC/cpttrs.f
index ed6b5c45..0f5db516 100644
--- a/SRC/cpttrs.f
+++ b/SRC/cpttrs.f
@@ -19,7 +19,7 @@
 *
 *  CPTTRS solves a tridiagonal system of the form
 *     A * X = B
-*  using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF.
+*  using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
 *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
 *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 *  the vector E, and X and B are N by NRHS matrices.
@@ -31,8 +31,8 @@
 *          Specifies the form of the factorization and whether the
 *          vector E is the superdiagonal of the upper bidiagonal factor
 *          U or the subdiagonal of the lower bidiagonal factor L.
-*          = 'U':  A = U'*D*U, E is the superdiagonal of U
-*          = 'L':  A = L*D*L', E is the subdiagonal of L
+*          = 'U':  A = U**H*D*U, E is the superdiagonal of U
+*          = 'L':  A = L*D*L**H, E is the subdiagonal of L
 *
 *  N       (input) INTEGER
 *          The order of the tridiagonal matrix A.  N >= 0.
@@ -43,13 +43,13 @@
 *
 *  D       (input) REAL array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          factorization A = U'*D*U or A = L*D*L'.
+*          factorization A = U**H*D*U or A = L*D*L**H.
 *
 *  E       (input) COMPLEX array, dimension (N-1)
 *          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
-*          bidiagonal factor U from the factorization A = U'*D*U.
+*          bidiagonal factor U from the factorization A = U**H*D*U.
 *          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
-*          bidiagonal factor L from the factorization A = L*D*L'.
+*          bidiagonal factor L from the factorization A = L*D*L**H.
 *
 *  B       (input/output) REAL array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
diff --git a/SRC/cptts2.f b/SRC/cptts2.f
index 46c5911d..6c2785f8 100644
--- a/SRC/cptts2.f
+++ b/SRC/cptts2.f
@@ -18,7 +18,7 @@
 *
 *  CPTTS2 solves a tridiagonal system of the form
 *     A * X = B
-*  using the factorization A = U'*D*U or A = L*D*L' computed by CPTTRF.
+*  using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
 *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
 *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 *  the vector E, and X and B are N by NRHS matrices.
@@ -30,8 +30,8 @@
 *          Specifies the form of the factorization and whether the
 *          vector E is the superdiagonal of the upper bidiagonal factor
 *          U or the subdiagonal of the lower bidiagonal factor L.
-*          = 1:  A = U'*D*U, E is the superdiagonal of U
-*          = 0:  A = L*D*L', E is the subdiagonal of L
+*          = 1:  A = U**H *D*U, E is the superdiagonal of U
+*          = 0:  A = L*D*L**H, E is the subdiagonal of L
 *
 *  N       (input) INTEGER
 *          The order of the tridiagonal matrix A.  N >= 0.
@@ -42,13 +42,13 @@
 *
 *  D       (input) REAL array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          factorization A = U'*D*U or A = L*D*L'.
+*          factorization A = U**H *D*U or A = L*D*L**H.
 *
 *  E       (input) COMPLEX array, dimension (N-1)
 *          If IUPLO = 1, the (n-1) superdiagonal elements of the unit
-*          bidiagonal factor U from the factorization A = U'*D*U.
+*          bidiagonal factor U from the factorization A = U**H*D*U.
 *          If IUPLO = 0, the (n-1) subdiagonal elements of the unit
-*          bidiagonal factor L from the factorization A = L*D*L'.
+*          bidiagonal factor L from the factorization A = L*D*L**H.
 *
 *  B       (input/output) REAL array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
@@ -81,14 +81,14 @@
 *
       IF( IUPLO.EQ.1 ) THEN
 *
-*        Solve A * X = B using the factorization A = U'*D*U,
+*        Solve A * X = B using the factorization A = U**H *D*U,
 *        overwriting each right hand side vector with its solution.
 *
          IF( NRHS.LE.2 ) THEN
             J = 1
     5       CONTINUE
 *
-*           Solve U' * x = b.
+*           Solve U**H * x = b.
 *
             DO 10 I = 2, N
                B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
@@ -109,7 +109,7 @@
          ELSE
             DO 60 J = 1, NRHS
 *
-*              Solve U' * x = b.
+*              Solve U**H * x = b.
 *
                DO 40 I = 2, N
                   B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
@@ -125,7 +125,7 @@
          END IF
       ELSE
 *
-*        Solve A * X = B using the factorization A = L*D*L',
+*        Solve A * X = B using the factorization A = L*D*L**H,
 *        overwriting each right hand side vector with its solution.
 *
          IF( NRHS.LE.2 ) THEN
@@ -138,7 +138,7 @@
                B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
    70       CONTINUE
 *
-*           Solve D * L' * x = b.
+*           Solve D * L**H * x = b.
 *
             DO 80 I = 1, N
                B( I, J ) = B( I, J ) / D( I )
@@ -159,7 +159,7 @@
                   B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
   100          CONTINUE
 *
-*              Solve D * L' * x = b.
+*              Solve D * L**H * x = b.
 *
                B( N, J ) = B( N, J ) / D( N )
                DO 110 I = N - 1, 1, -1
diff --git a/SRC/cspcon.f b/SRC/cspcon.f
index c3ea45e9..e9074613 100644
--- a/SRC/cspcon.f
+++ b/SRC/cspcon.f
@@ -142,7 +142,7 @@
       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL CSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/cspsv.f b/SRC/cspsv.f
index cbdbbfea..c26d2c4b 100644
--- a/SRC/cspsv.f
+++ b/SRC/cspsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL CSPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/cspsvx.f b/SRC/cspsvx.f
index eb6304fb..6db4603e 100644
--- a/SRC/cspsvx.f
+++ b/SRC/cspsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL CCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL CSPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/csptrf.f b/SRC/csptrf.f
index bdd28572..9eac37f3 100644
--- a/SRC/csptrf.f
+++ b/SRC/csptrf.f
@@ -72,7 +72,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -89,7 +89,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -162,7 +162,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -283,7 +283,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = CONE / AP( KC+K-1 )
                CALL CSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -302,8 +302,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -348,7 +348,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -476,7 +476,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = CONE / AP( KC )
                   CALL CSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -499,8 +499,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/csptri.f b/SRC/csptri.f
index 07eeab15..81bf98da 100644
--- a/SRC/csptri.f
+++ b/SRC/csptri.f
@@ -128,7 +128,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -229,7 +229,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/csptrs.f b/SRC/csptrs.f
index 753a0c36..bc71d28f 100644
--- a/SRC/csptrs.f
+++ b/SRC/csptrs.f
@@ -103,7 +103,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -177,7 +177,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -212,7 +212,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -234,7 +234,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -311,7 +311,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -330,7 +330,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -347,7 +347,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/csycon.f b/SRC/csycon.f
index 5b40df5d..1aff138a 100644
--- a/SRC/csycon.f
+++ b/SRC/csycon.f
@@ -146,7 +146,7 @@
       CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL CSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/csysv.f b/SRC/csysv.f
index faa99004..c54c41cc 100644
--- a/SRC/csysv.f
+++ b/SRC/csysv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL CSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/csysvx.f b/SRC/csysvx.f
index b73ad9a8..0194337f 100644
--- a/SRC/csysvx.f
+++ b/SRC/csysvx.f
@@ -255,7 +255,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL CLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL CSYTRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/csytf2.f b/SRC/csytf2.f
index 64be1664..7534c7f9 100644
--- a/SRC/csytf2.f
+++ b/SRC/csytf2.f
@@ -20,10 +20,10 @@
 *  CSYTF2 computes the factorization of a complex symmetric matrix A
 *  using the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**T  or  A = L*D*L**T
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the transpose of U, and D is symmetric and
+*  triangular matrices, U**T is the transpose of U, and D is symmetric and
 *  block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -87,7 +87,7 @@
 *  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -178,7 +178,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -284,7 +284,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = CONE / A( K, K )
                CALL CSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -303,8 +303,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -346,7 +346,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -455,7 +455,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = CONE / A( K, K )
                   CALL CSYR( UPLO, N-K, -R1, A( K+1, K ), 1,
@@ -473,8 +473,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/csytrf.f b/SRC/csytrf.f
index 2084d964..a3dac79f 100644
--- a/SRC/csytrf.f
+++ b/SRC/csytrf.f
@@ -87,7 +87,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -187,7 +187,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by CLASYF;
@@ -227,7 +227,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by CLASYF;
diff --git a/SRC/csytri.f b/SRC/csytri.f
index 8b54abe9..d2de840c 100644
--- a/SRC/csytri.f
+++ b/SRC/csytri.f
@@ -128,7 +128,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -217,7 +217,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/csytri2x.f b/SRC/csytri2x.f
index a10661ba..489bf452 100644
--- a/SRC/csytri2x.f
+++ b/SRC/csytri2x.f
@@ -154,7 +154,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
         CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -182,9 +182,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -309,7 +309,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -331,7 +331,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
          CALL CTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -359,9 +359,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -492,7 +492,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/csytrs.f b/SRC/csytrs.f
index 4f230619..c4233a37 100644
--- a/SRC/csytrs.f
+++ b/SRC/csytrs.f
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -178,7 +178,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -211,7 +211,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL CGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -232,7 +232,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -306,7 +306,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -323,7 +323,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -340,7 +340,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/csytrs2.f b/SRC/csytrs2.f
index d90ff478..abe7079e 100644
--- a/SRC/csytrs2.f
+++ b/SRC/csytrs2.f
@@ -117,9 +117,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
-*       P' * B  
+*       P**T * B  
         K=N
         DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN
@@ -139,11 +139,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL CTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -167,11 +167,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**T \ B) -> B   [ U**T \ (D \ (U \P**T * B) ) ]
 *
          CALL CTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**T \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -194,9 +194,9 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
-*       P' * B  
+*       P**T * B  
         K=1
         DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN
@@ -216,11 +216,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL CTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -242,11 +242,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**T \ B) -> B   [ L**T \ (D \ (L \P**T * B) ) ]
 * 
         CALL CTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**T \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/ctgex2.f b/SRC/ctgex2.f
index 8114b092..8008ea32 100644
--- a/SRC/ctgex2.f
+++ b/SRC/ctgex2.f
@@ -28,8 +28,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
+*         Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
 *
 *
 *  Arguments
@@ -213,7 +213,7 @@
       IF( WANDS ) THEN
 *
 *        Strong stability test:
-*           F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A, B)))
+*           F-norm((A-QL**H*S*QR, B-QL**H*T*QR)) <= O(EPS*F-norm((A, B)))
 *
          CALL CLACPY( 'Full', M, M, S, LDST, WORK, M )
          CALL CLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )
diff --git a/SRC/ctgexc.f b/SRC/ctgexc.f
index e0484355..06f3c7a5 100644
--- a/SRC/ctgexc.f
+++ b/SRC/ctgexc.f
@@ -29,8 +29,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
+*         Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
 *
 *  Arguments
 *  =========
diff --git a/SRC/ctgsen.f b/SRC/ctgsen.f
index 8312f2f5..de9b77e6 100644
--- a/SRC/ctgsen.f
+++ b/SRC/ctgsen.f
@@ -28,7 +28,7 @@
 *
 *  CTGSEN reorders the generalized Schur decomposition of a complex
 *  matrix pair (A, B) (in terms of an unitary equivalence trans-
-*  formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues
+*  formation Q**H * (A, B) * Z), so that a selected cluster of eigenvalues
 *  appears in the leading diagonal blocks of the pair (A,B). The leading
 *  columns of Q and Z form unitary bases of the corresponding left and
 *  right eigenspaces (deflating subspaces). (A, B) must be in
@@ -197,11 +197,11 @@
 *  U and W that move them to the top left corner of (A, B). In other
 *  words, the selected eigenvalues are the eigenvalues of (A11, B11) in
 *
-*                U'*(A, B)*W = (A11 A12) (B11 B12) n1
+*              U**H*(A, B)*W = (A11 A12) (B11 B12) n1
 *                              ( 0  A22),( 0  B22) n2
 *                                n1  n2    n1  n2
 *
-*  where N = n1+n2 and U' means the conjugate transpose of U. The first
+*  where N = n1+n2 and U**H means the conjugate transpose of U. The first
 *  n1 columns of U and W span the specified pair of left and right
 *  eigenspaces (deflating subspaces) of (A, B).
 *
@@ -209,7 +209,7 @@
 *  decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the
 *  reordered generalized Schur form of (C, D) is given by
 *
-*           (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',
+*           (C, D) = (Q*U)*(U**H *(A, B)*W)*(Z*W)**H,
 *
 *  and the first n1 columns of Q*U and Z*W span the corresponding
 *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).
diff --git a/SRC/ctgsja.f b/SRC/ctgsja.f
index 9a14ff61..3f07b22b 100644
--- a/SRC/ctgsja.f
+++ b/SRC/ctgsja.f
@@ -48,10 +48,10 @@
 *
 *  On exit,
 *
-*         U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R ),
+*         U**H *A*Q = D1*( 0 R ),    V**H *B*Q = D2*( 0 R ),
 *
-*  where U, V and Q are unitary matrices, Z' denotes the conjugate
-*  transpose of Z, R is a nonsingular upper triangular matrix, and D1
+*  where U, V and Q are unitary matrices.
+*  R is a nonsingular upper triangular matrix, and D1
 *  and D2 are ``diagonal'' matrices, which are of the following
 *  structures:
 *
@@ -248,10 +248,10 @@
 *  min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
 *  matrix B13 to the form:
 *
-*           U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
+*           U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
 *
-*  where U1, V1 and Q1 are unitary matrix, and Z' is the conjugate
-*  transpose of Z.  C1 and S1 are diagonal matrices satisfying
+*  where U1, V1 and Q1 are unitary matrix.
+*  C1 and S1 are diagonal matrices satisfying
 *
 *                C1**2 + S1**2 = I,
 *
@@ -372,13 +372,13 @@
                CALL CLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
      $                      CSV, SNV, CSQ, SNQ )
 *
-*              Update (K+I)-th and (K+J)-th rows of matrix A: U'*A
+*              Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
 *
                IF( K+J.LE.M )
      $            CALL CROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
      $                       LDA, CSU, CONJG( SNU ) )
 *
-*              Update I-th and J-th rows of matrix B: V'*B
+*              Update I-th and J-th rows of matrix B: V**H *B
 *
                CALL CROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
      $                    CSV, CONJG( SNV ) )
diff --git a/SRC/ctgsna.f b/SRC/ctgsna.f
index 37c11e31..1e832e4a 100644
--- a/SRC/ctgsna.f
+++ b/SRC/ctgsna.f
@@ -132,12 +132,12 @@
 *  The reciprocal of the condition number of the i-th generalized
 *  eigenvalue w = (a, b) is defined as
 *
-*          S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v))
+*          S(I) = (|v**HAu|**2 + |v**HBu|**2)**(1/2) / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of (A, B)
 *  corresponding to w; |z| denotes the absolute value of the complex
 *  number, and norm(u) denotes the 2-norm of the vector u. The pair
-*  (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the
+*  (a, b) corresponds to an eigenvalue w = a/b (= v**HAu/v**HBu) of the
 *  matrix pair (A, B). If both a and b equal zero, then (A,B) is
 *  singular and S(I) = -1 is returned.
 *
@@ -166,7 +166,7 @@
 *         Zl = [ kron(a, In-1) -kron(1, A22) ]
 *              [ kron(b, In-1) -kron(1, B22) ].
 *
-*  Here In-1 is the identity matrix of size n-1 and X' is the conjugate
+*  Here In-1 is the identity matrix of size n-1 and X**H is the conjugate
 *  transpose of X. kron(X, Y) is the Kronecker product between the
 *  matrices X and Y.
 *
diff --git a/SRC/ctgsy2.f b/SRC/ctgsy2.f
index b762b234..a9fdf836 100644
--- a/SRC/ctgsy2.f
+++ b/SRC/ctgsy2.f
@@ -298,7 +298,7 @@
       ELSE
 *
 *        Solve transposed (I, J) - system:
-*           A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J)
+*           A(I, I)**H * R(I, J) + D(I, I)**H * L(J, J) = C(I, J)
 *           R(I, I) * B(J, J) + L(I, J) * E(J, J)   = -F(I, J)
 *        for I = 1, 2, ..., M, J = N, N - 1, ..., 1
 *
diff --git a/SRC/ctgsyl.f b/SRC/ctgsyl.f
index 333cbcea..2d3374ca 100644
--- a/SRC/ctgsyl.f
+++ b/SRC/ctgsyl.f
@@ -46,11 +46,11 @@
 *  transpose of X. Kron(X, Y) is the Kronecker product between the
 *  matrices X and Y.
 *
-*  If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b
+*  If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
 *  is solved for, which is equivalent to solve for R and L in
 *
-*              A' * R + D' * L = scale * C           (3)
-*              R * B' + L * E' = scale * -F
+*              A**H * R + D**H * L = scale * C           (3)
+*              R * B**H + L * E**H = scale * -F
 *
 *  This case (TRANS = 'C') is used to compute an one-norm-based estimate
 *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
@@ -490,7 +490,7 @@
       ELSE
 *
 *        Solve transposed (I, J)-subsystem
-*            A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J)
+*            A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J)
 *            R(I, J) * B(J, J)  + L(I, J) * E(J, J) = -F(I, J)
 *        for I = 1,2,..., P; J = Q, Q-1,..., 1
 *
diff --git a/SRC/ctrevc.f b/SRC/ctrevc.f
index 900248f0..9bfe2b93 100644
--- a/SRC/ctrevc.f
+++ b/SRC/ctrevc.f
@@ -332,7 +332,7 @@
    90       CONTINUE
 *
 *           Solve the triangular system:
-*              (T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK.
+*              (T(KI+1:N,KI+1:N) - T(KI,KI))**H*X = SCALE*WORK.
 *
             DO 100 K = KI + 1, N
                T( K, K ) = T( K, K ) - T( KI, KI )
diff --git a/SRC/ctrsen.f b/SRC/ctrsen.f
index 2b35ef3c..a5eb9d70 100644
--- a/SRC/ctrsen.f
+++ b/SRC/ctrsen.f
@@ -119,16 +119,16 @@
 *  transformation Z to move them to the top left corner of T. In other
 *  words, the selected eigenvalues are the eigenvalues of T11 in:
 *
-*                Z'*T*Z = ( T11 T12 ) n1
+*          Z**H * T * Z = ( T11 T12 ) n1
 *                         (  0  T22 ) n2
 *                            n1  n2
 *
-*  where N = n1+n2 and Z' means the conjugate transpose of Z. The first
+*  where N = n1+n2. The first
 *  n1 columns of Z span the specified invariant subspace of T.
 *
 *  If T has been obtained from the Schur factorization of a matrix
-*  A = Q*T*Q', then the reordered Schur factorization of A is given by
-*  A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span the
+*  A = Q*T*Q**H, then the reordered Schur factorization of A is given by
+*  A = (Q*Z)*(Z**H*T*Z)*(Q*Z)**H, and the first n1 columns of Q*Z span the
 *  corresponding invariant subspace of A.
 *
 *  The reciprocal condition number of the average of the eigenvalues of
@@ -331,7 +331,7 @@
      $                      IERR )
             ELSE
 *
-*              Solve T11'*R - R*T22' = scale*X.
+*              Solve T11**H*R - R*T22**H = scale*X.
 *
                CALL CTRSYL( 'C', 'C', -1, N1, N2, T, LDT,
      $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
diff --git a/SRC/ctrsna.f b/SRC/ctrsna.f
index f538b7db..6ed7f961 100644
--- a/SRC/ctrsna.f
+++ b/SRC/ctrsna.f
@@ -124,10 +124,10 @@
 *  The reciprocal of the condition number of an eigenvalue lambda is
 *  defined as
 *
-*          S(lambda) = |v'*u| / (norm(u)*norm(v))
+*          S(lambda) = |v**H*u| / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of T corresponding
-*  to lambda; v' denotes the conjugate transpose of v, and norm(u)
+*  to lambda; v**H denotes the conjugate transpose of v, and norm(u)
 *  denotes the Euclidean norm. These reciprocal condition numbers always
 *  lie between zero (very badly conditioned) and one (very well
 *  conditioned). If n = 1, S(lambda) is defined to be 1.
@@ -303,7 +303,7 @@
                WORK( I, I ) = WORK( I, I ) - WORK( 1, 1 )
    20       CONTINUE
 *
-*           Estimate a lower bound for the 1-norm of inv(C'). The 1st
+*           Estimate a lower bound for the 1-norm of inv(C**H). The 1st
 *           and (N+1)th columns of WORK are used to store work vectors.
 *
             SEP( KS ) = ZERO
@@ -316,7 +316,7 @@
             IF( KASE.NE.0 ) THEN
                IF( KASE.EQ.1 ) THEN
 *
-*                 Solve C'*x = scale*b
+*                 Solve C**H*x = scale*b
 *
                   CALL CLATRS( 'Upper', 'Conjugate transpose',
      $                         'Nonunit', NORMIN, N-1, WORK( 2, 2 ),
diff --git a/SRC/ctrsyl.f b/SRC/ctrsyl.f
index 721c5849..28c930c3 100644
--- a/SRC/ctrsyl.f
+++ b/SRC/ctrsyl.f
@@ -209,17 +209,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
 *
-*        Solve    A' *X + ISGN*X*B = scale*C.
+*        Solve    A**H *X + ISGN*X*B = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-left corner column by column by
 *
-*            A'(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
+*            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
 *
 *        Where
-*                   K-1                         L-1
-*          R(K,L) = SUM [A'(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
-*                   I=1                         J=1
+*                   K-1                           L-1
+*          R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
+*                   I=1                           J=1
 *
          DO 60 L = 1, N
             DO 50 K = 1, M
@@ -257,19 +257,19 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A'*X + ISGN*X*B' = C.
+*        Solve    A**H*X + ISGN*X*B**H = C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-right corner column by column by
 *
-*            A'(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+*            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
 *
 *        Where
 *                    K-1
-*           R(K,L) = SUM [A'(I,K)*X(I,L)] +
+*           R(K,L) = SUM [A**H(I,K)*X(I,L)] +
 *                    I=1
 *                           N
-*                     ISGN*SUM [X(K,J)*B'(L,J)].
+*                     ISGN*SUM [X(K,J)*B**H(L,J)].
 *                          J=L+1
 *
          DO 90 L = N, 1, -1
@@ -309,16 +309,16 @@
 *
       ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A*X + ISGN*X*B' = C.
+*        Solve    A*X + ISGN*X*B**H = C.
 *
 *        The (K,L)th block of X is determined starting from
 *        bottom-left corner column by column by
 *
-*           A(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+*           A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
 *
 *        Where
 *                    M                          N
-*          R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B'(L,J)]
+*          R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
 *                  I=K+1                      J=L+1
 *
          DO 120 L = N, 1, -1
diff --git a/SRC/ctzrqf.f b/SRC/ctzrqf.f
index a98aebd3..3e90546d 100644
--- a/SRC/ctzrqf.f
+++ b/SRC/ctzrqf.f
@@ -66,9 +66,9 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
-*                                                 (   0    )
-*                                                 ( z( k ) )
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
+*                                                   (   0    )
+*                                                   ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an ( n - m ) element vector.
 *  tau and z( k ) are chosen to annihilate the elements of the kth row
@@ -142,7 +142,7 @@
 *
             IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
 *
-*              We now perform the operation  A := A*P( k )'.
+*              We now perform the operation  A := A*P( k )**H.
 *
 *              Use the first ( k - 1 ) elements of TAU to store  a( k ),
 *              where  a( k ) consists of the first ( k - 1 ) elements of
@@ -157,7 +157,7 @@
      $                     LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
 *
 *              Now form  a( k ) := a( k ) - conjg(tau)*w
-*              and       B      := B      - conjg(tau)*w*z( k )'.
+*              and       B      := B      - conjg(tau)*w*z( k )**H.
 *
                CALL CAXPY( K-1, -CONJG( TAU( K ) ), TAU, 1, A( 1, K ),
      $                     1 )
diff --git a/SRC/ctzrzf.f b/SRC/ctzrzf.f
index bcdf4221..7afbbd22 100644
--- a/SRC/ctzrzf.f
+++ b/SRC/ctzrzf.f
@@ -81,7 +81,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/cungl2.f b/SRC/cungl2.f
index daf16e04..03e2967e 100644
--- a/SRC/cungl2.f
+++ b/SRC/cungl2.f
@@ -19,7 +19,7 @@
 *  which is defined as the first m rows of a product of k elementary
 *  reflectors of order n
 *
-*        Q  =  H(k)' . . . H(2)' H(1)'
+*        Q  =  H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by CGELQF.
 *
@@ -110,7 +110,7 @@
 *
       DO 40 I = K, 1, -1
 *
-*        Apply H(i)' to A(i:m,i:n) from the right
+*        Apply H(i)**H to A(i:m,i:n) from the right
 *
          IF( I.LT.N ) THEN
             CALL CLACGV( N-I, A( I, I+1 ), LDA )
diff --git a/SRC/cunglq.f b/SRC/cunglq.f
index ef32e5c7..c1809407 100644
--- a/SRC/cunglq.f
+++ b/SRC/cunglq.f
@@ -19,7 +19,7 @@
 *  which is defined as the first M rows of a product of K elementary
 *  reflectors of order N
 *
-*        Q  =  H(k)' . . . H(2)' H(1)'
+*        Q  =  H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by CGELQF.
 *
@@ -185,7 +185,7 @@
                CALL CLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
      $                      LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i+ib:m,i:n) from the right
+*              Apply H**H to A(i+ib:m,i:n) from the right
 *
                CALL CLARFB( 'Right', 'Conjugate transpose', 'Forward',
      $                      'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
@@ -193,7 +193,7 @@
      $                      WORK( IB+1 ), LDWORK )
             END IF
 *
-*           Apply H' to columns i:n of current block
+*           Apply H**H to columns i:n of current block
 *
             CALL CUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
      $                   IINFO )
diff --git a/SRC/cungr2.f b/SRC/cungr2.f
index 4e75e51d..3f104be3 100644
--- a/SRC/cungr2.f
+++ b/SRC/cungr2.f
@@ -19,7 +19,7 @@
 *  which is defined as the last m rows of a product of k elementary
 *  reflectors of order n
 *
-*        Q  =  H(1)' H(2)' . . . H(k)'
+*        Q  =  H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by CGERQF.
 *
@@ -112,7 +112,7 @@
       DO 40 I = 1, K
          II = M - K + I
 *
-*        Apply H(i)' to A(1:m-k+i,1:n-k+i) from the right
+*        Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
 *
          CALL CLACGV( N-M+II-1, A( II, 1 ), LDA )
          A( II, N-M+II ) = ONE
diff --git a/SRC/cungrq.f b/SRC/cungrq.f
index bd9c416f..a09442c5 100644
--- a/SRC/cungrq.f
+++ b/SRC/cungrq.f
@@ -19,7 +19,7 @@
 *  which is defined as the last M rows of a product of K elementary
 *  reflectors of order N
 *
-*        Q  =  H(1)' H(2)' . . . H(k)'
+*        Q  =  H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by CGERQF.
 *
@@ -193,7 +193,7 @@
                CALL CLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
      $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
+*              Apply H**H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
 *
                CALL CLARFB( 'Right', 'Conjugate transpose', 'Backward',
      $                      'Rowwise', II-1, N-K+I+IB-1, IB, A( II, 1 ),
@@ -201,7 +201,7 @@
      $                      LDWORK )
             END IF
 *
-*           Apply H' to columns 1:n-k+i+ib-1 of current block
+*           Apply H**H to columns 1:n-k+i+ib-1 of current block
 *
             CALL CUNGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
      $                   WORK, IINFO )
diff --git a/SRC/cunm2l.f b/SRC/cunm2l.f
index 06904231..6aebcaff 100644
--- a/SRC/cunm2l.f
+++ b/SRC/cunm2l.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -168,17 +168,17 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(1:m-k+i,1:n)
+*           H(i) or H(i)**H is applied to C(1:m-k+i,1:n)
 *
             MI = M - K + I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,1:n-k+i)
+*           H(i) or H(i)**H is applied to C(1:m,1:n-k+i)
 *
             NI = N - K + I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/cunm2r.f b/SRC/cunm2r.f
index f710288f..69f22ae3 100644
--- a/SRC/cunm2r.f
+++ b/SRC/cunm2r.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -170,19 +170,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/cunml2.f b/SRC/cunml2.f
index e923d92e..191656d7 100644
--- a/SRC/cunml2.f
+++ b/SRC/cunml2.f
@@ -21,16 +21,16 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(k)' . . . H(2)' H(1)'
+*        Q = H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n
 *  if SIDE = 'R'.
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -170,19 +170,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = CONJG( TAU( I ) )
diff --git a/SRC/cunmlq.f b/SRC/cunmlq.f
index acc4c173..c700d856 100644
--- a/SRC/cunmlq.f
+++ b/SRC/cunmlq.f
@@ -27,7 +27,7 @@
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(k)' . . . H(2)' H(1)'
+*        Q = H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N
 *  if SIDE = 'R'.
@@ -242,19 +242,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL CLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
diff --git a/SRC/cunmql.f b/SRC/cunmql.f
index 23128473..cf448bb3 100644
--- a/SRC/cunmql.f
+++ b/SRC/cunmql.f
@@ -238,17 +238,17 @@
      $                   A( 1, I ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**H is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**H is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL CLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
      $                   IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/cunmqr.f b/SRC/cunmqr.f
index 0e7da561..0215f28b 100644
--- a/SRC/cunmqr.f
+++ b/SRC/cunmqr.f
@@ -235,19 +235,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL CLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
      $                   IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
diff --git a/SRC/cunmr2.f b/SRC/cunmr2.f
index e1fc7f08..cea18732 100644
--- a/SRC/cunmr2.f
+++ b/SRC/cunmr2.f
@@ -21,16 +21,16 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(1)' H(2)' . . . H(k)'
+*        Q = H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by CGERQF. Q is of order m if SIDE = 'L' and of order n
 *  if SIDE = 'R'.
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -168,17 +168,17 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(1:m-k+i,1:n)
+*           H(i) or H(i)**H is applied to C(1:m-k+i,1:n)
 *
             MI = M - K + I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,1:n-k+i)
+*           H(i) or H(i)**H is applied to C(1:m,1:n-k+i)
 *
             NI = N - K + I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = CONJG( TAU( I ) )
diff --git a/SRC/cunmr3.f b/SRC/cunmr3.f
index a9f6321f..ce440abd 100644
--- a/SRC/cunmr3.f
+++ b/SRC/cunmr3.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -80,7 +80,7 @@
 *
 *  C       (input/output) COMPLEX array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -182,19 +182,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/cunmrq.f b/SRC/cunmrq.f
index 3ed1cbe1..54cea54c 100644
--- a/SRC/cunmrq.f
+++ b/SRC/cunmrq.f
@@ -27,7 +27,7 @@
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(1)' H(2)' . . . H(k)'
+*        Q = H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by CGERQF. Q is of order M if SIDE = 'L' and of order N
 *  if SIDE = 'R'.
@@ -245,17 +245,17 @@
      $                   A( I, 1 ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**H is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**H is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL CLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/cunmrz.f b/SRC/cunmrz.f
index 55b62623..26c224a6 100644
--- a/SRC/cunmrz.f
+++ b/SRC/cunmrz.f
@@ -268,19 +268,19 @@
 *
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL CLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
diff --git a/SRC/cupmtr.f b/SRC/cupmtr.f
index 6d6e893c..c5ab2e9e 100644
--- a/SRC/cupmtr.f
+++ b/SRC/cupmtr.f
@@ -170,17 +170,17 @@
          DO 10 I = I1, I2, I3
             IF( LEFT ) THEN
 *
-*              H(i) or H(i)' is applied to C(1:i,1:n)
+*              H(i) or H(i)**H is applied to C(1:i,1:n)
 *
                MI = I
             ELSE
 *
-*              H(i) or H(i)' is applied to C(1:m,1:i)
+*              H(i) or H(i)**H is applied to C(1:m,1:i)
 *
                NI = I
             END IF
 *
-*           Apply H(i) or H(i)'
+*           Apply H(i) or H(i)**H
 *
             IF( NOTRAN ) THEN
                TAUI = TAU( I )
@@ -231,19 +231,19 @@
             AP( II ) = ONE
             IF( LEFT ) THEN
 *
-*              H(i) or H(i)' is applied to C(i+1:m,1:n)
+*              H(i) or H(i)**H is applied to C(i+1:m,1:n)
 *
                MI = M - I
                IC = I + 1
             ELSE
 *
-*              H(i) or H(i)' is applied to C(1:m,i+1:n)
+*              H(i) or H(i)**H is applied to C(1:m,i+1:n)
 *
                NI = N - I
                JC = I + 1
             END IF
 *
-*           Apply H(i) or H(i)'
+*           Apply H(i) or H(i)**H
 *
             IF( NOTRAN ) THEN
                TAUI = TAU( I )
diff --git a/SRC/dgbbrd.f b/SRC/dgbbrd.f
index 5cefa7f1..12f0d8f8 100644
--- a/SRC/dgbbrd.f
+++ b/SRC/dgbbrd.f
@@ -19,20 +19,20 @@
 *  =======
 *
 *  DGBBRD reduces a real general m-by-n band matrix A to upper
-*  bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
+*  bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
 *
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
+*  The routine computes B, and optionally forms Q or P**T, or computes
+*  Q**T*C for a given matrix C.
 *
 *  Arguments
 *  =========
 *
 *  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
+*          Specifies whether or not the matrices Q and P**T are to be
 *          formed.
-*          = 'N': do not form Q or P';
+*          = 'N': do not form Q or P**T;
 *          = 'Q': form Q only;
-*          = 'P': form P' only;
+*          = 'P': form P**T only;
 *          = 'B': form both.
 *
 *  M       (input) INTEGER
@@ -85,7 +85,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,NCC)
 *          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
+*          On exit, C is overwritten by Q**T*C.
 *          C is not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
@@ -157,7 +157,7 @@
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**T to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL DLASET( 'Full', M, M, ZERO, ONE, Q, LDQ )
@@ -334,7 +334,7 @@
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**T
 *
                   DO 60 J = J1, J2, KB1
                      CALL DROT( N, PT( J+KUN-1, 1 ), LDPT,
diff --git a/SRC/dgbcon.f b/SRC/dgbcon.f
index 1e43d4da..7596cf5c 100644
--- a/SRC/dgbcon.f
+++ b/SRC/dgbcon.f
@@ -179,13 +179,13 @@
      $                   INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             IF( LNOTI ) THEN
                DO 30 J = N - 1, 1, -1
diff --git a/SRC/dgebd2.f b/SRC/dgebd2.f
index df13baaa..5807773b 100644
--- a/SRC/dgebd2.f
+++ b/SRC/dgebd2.f
@@ -87,7 +87,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
diff --git a/SRC/dgebrd.f b/SRC/dgebrd.f
index eb6b6f5d..737d85c5 100644
--- a/SRC/dgebrd.f
+++ b/SRC/dgebrd.f
@@ -99,7 +99,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
@@ -112,7 +112,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
@@ -232,7 +232,7 @@
      $                WORK( LDWRKX*NB+1 ), LDWRKY )
 *
 *        Update the trailing submatrix A(i+nb:m,i+nb:n), using an update
-*        of the form  A := A - V*Y' - X*U'
+*        of the form  A := A - V*Y**T - X*U**T
 *
          CALL DGEMM( 'No transpose', 'Transpose', M-I-NB+1, N-I-NB+1,
      $               NB, -ONE, A( I+NB, I ), LDA,
diff --git a/SRC/dgecon.f b/SRC/dgecon.f
index b49a91f6..207ca98e 100644
--- a/SRC/dgecon.f
+++ b/SRC/dgecon.f
@@ -149,12 +149,12 @@
      $                   A, LDA, WORK, SU, WORK( 3*N+1 ), INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SU, WORK( 3*N+1 ), INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL DLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A,
      $                   LDA, WORK, SL, WORK( 2*N+1 ), INFO )
diff --git a/SRC/dgeev.f b/SRC/dgeev.f
index 8f8d0b82..98cae6de 100644
--- a/SRC/dgeev.f
+++ b/SRC/dgeev.f
@@ -25,8 +25,8 @@
 *                   A * v(j) = lambda(j) * v(j)
 *  where lambda(j) is its eigenvalue.
 *  The left eigenvector u(j) of A satisfies
-*                u(j)**H * A = lambda(j) * u(j)**H
-*  where u(j)**H denotes the conjugate transpose of u(j).
+*                u(j)**T * A = lambda(j) * u(j)**T
+*  where u(j)**T denotes the transpose of u(j).
 *
 *  The computed eigenvectors are normalized to have Euclidean norm
 *  equal to 1 and largest component real.
diff --git a/SRC/dgeevx.f b/SRC/dgeevx.f
index 2f914fa9..0632f0a6 100644
--- a/SRC/dgeevx.f
+++ b/SRC/dgeevx.f
@@ -35,8 +35,8 @@
 *                   A * v(j) = lambda(j) * v(j)
 *  where lambda(j) is its eigenvalue.
 *  The left eigenvector u(j) of A satisfies
-*                u(j)**H * A = lambda(j) * u(j)**H
-*  where u(j)**H denotes the conjugate transpose of u(j).
+*                u(j)**T * A = lambda(j) * u(j)**T
+*  where u(j)**T denotes the transpose of u(j).
 *
 *  The computed eigenvectors are normalized to have Euclidean norm
 *  equal to 1 and largest component real.
diff --git a/SRC/dgehd2.f b/SRC/dgehd2.f
index 8853657c..e182e5f9 100644
--- a/SRC/dgehd2.f
+++ b/SRC/dgehd2.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  DGEHD2 reduces a real general matrix A to upper Hessenberg form H by
-*  an orthogonal similarity transformation:  Q' * A * Q = H .
+*  an orthogonal similarity transformation:  Q**T * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -63,7 +63,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
diff --git a/SRC/dgehrd.f b/SRC/dgehrd.f
index 0cdfdd06..f3dc4505 100644
--- a/SRC/dgehrd.f
+++ b/SRC/dgehrd.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  DGEHRD reduces a real general matrix A to upper Hessenberg form H by
-*  an orthogonal similarity transformation:  Q' * A * Q = H .
+*  an orthogonal similarity transformation:  Q**T * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -223,14 +223,14 @@
             IB = MIN( NB, IHI-I )
 *
 *           Reduce columns i:i+ib-1 to Hessenberg form, returning the
-*           matrices V and T of the block reflector H = I - V*T*V'
+*           matrices V and T of the block reflector H = I - V*T*V**T
 *           which performs the reduction, and also the matrix Y = A*V*T
 *
             CALL DLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
      $                   WORK, LDWORK )
 *
 *           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
+*           right, computing  A := A - Y * V**T. V(i+ib,ib-1) must be set
 *           to 1
 *
             EI = A( I+IB, I+IB-1 )
diff --git a/SRC/dgelq2.f b/SRC/dgelq2.f
index 823dc16c..8ca127e3 100644
--- a/SRC/dgelq2.f
+++ b/SRC/dgelq2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
diff --git a/SRC/dgelqf.f b/SRC/dgelqf.f
index 6e67d40a..14590518 100644
--- a/SRC/dgelqf.f
+++ b/SRC/dgelqf.f
@@ -68,7 +68,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
diff --git a/SRC/dgels.f b/SRC/dgels.f
index dc9a92fb..53d3fc6b 100644
--- a/SRC/dgels.f
+++ b/SRC/dgels.f
@@ -277,7 +277,7 @@
 *
 *           Least-Squares Problem min || A * X - B ||
 *
-*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
             CALL DORMQR( 'Left', 'Transpose', M, NRHS, N, A, LDA,
      $                   WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
@@ -359,7 +359,7 @@
    30          CONTINUE
    40       CONTINUE
 *
-*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS)
+*           B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS)
 *
             CALL DORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA,
      $                   WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
diff --git a/SRC/dgelsx.f b/SRC/dgelsx.f
index e9194c81..da7b0ce8 100644
--- a/SRC/dgelsx.f
+++ b/SRC/dgelsx.f
@@ -44,8 +44,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**T [ inv(T11)*Q1**T*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  Arguments
@@ -267,7 +267,7 @@
 *
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
       CALL DORM2R( 'Left', 'Transpose', M, NRHS, MN, A, LDA, WORK( 1 ),
      $             B, LDB, WORK( 2*MN+1 ), INFO )
@@ -285,7 +285,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          DO 50 I = 1, RANK
diff --git a/SRC/dgelsy.f b/SRC/dgelsy.f
index 9b5a7844..4200e4d9 100644
--- a/SRC/dgelsy.f
+++ b/SRC/dgelsy.f
@@ -42,8 +42,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**T [ inv(T11)*Q1**T*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  This routine is basically identical to the original xGELSX except
@@ -325,7 +325,7 @@
 *     workspace: 2*MN.
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
       CALL DORMQR( 'Left', 'Transpose', M, NRHS, MN, A, LDA, WORK( 1 ),
      $             B, LDB, WORK( 2*MN+1 ), LWORK-2*MN, INFO )
@@ -344,7 +344,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          CALL DORMRZ( 'Left', 'Transpose', N, NRHS, RANK, N-RANK, A,
diff --git a/SRC/dgeql2.f b/SRC/dgeql2.f
index f8037028..4e7e724a 100644
--- a/SRC/dgeql2.f
+++ b/SRC/dgeql2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
diff --git a/SRC/dgeqlf.f b/SRC/dgeqlf.f
index 989468b6..9c5edc1c 100644
--- a/SRC/dgeqlf.f
+++ b/SRC/dgeqlf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -186,7 +186,7 @@
                CALL DLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
      $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
+*              Apply H**T to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
 *
                CALL DLARFB( 'Left', 'Transpose', 'Backward',
      $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
diff --git a/SRC/dgeqp3.f b/SRC/dgeqp3.f
index aa471606..fa65ffe5 100644
--- a/SRC/dgeqp3.f
+++ b/SRC/dgeqp3.f
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real/complex scalar, and v is a real/complex vector
 *  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
diff --git a/SRC/dgeqpf.f b/SRC/dgeqpf.f
index e704d43e..3809cf41 100644
--- a/SRC/dgeqpf.f
+++ b/SRC/dgeqpf.f
@@ -66,7 +66,7 @@
 *
 *  Each H(i) has the form
 *
-*     H = I - tau * v * v'
+*     H = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
diff --git a/SRC/dgeqr2.f b/SRC/dgeqr2.f
index f21bb799..aa18f8f9 100644
--- a/SRC/dgeqr2.f
+++ b/SRC/dgeqr2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
diff --git a/SRC/dgeqr2p.f b/SRC/dgeqr2p.f
index b1bd36c9..767ea3a0 100644
--- a/SRC/dgeqr2p.f
+++ b/SRC/dgeqr2p.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
diff --git a/SRC/dgeqrf.f b/SRC/dgeqrf.f
index c6bd63fc..3d1392de 100644
--- a/SRC/dgeqrf.f
+++ b/SRC/dgeqrf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**T to A(i:m,i+ib:n) from the left
 *
                CALL DLARFB( 'Left', 'Transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/dgeqrfp.f b/SRC/dgeqrfp.f
index 862de903..1960972f 100644
--- a/SRC/dgeqrfp.f
+++ b/SRC/dgeqrfp.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**T to A(i:m,i+ib:n) from the left
 *
                CALL DLARFB( 'Left', 'Transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/dgerq2.f b/SRC/dgerq2.f
index d7917508..aff63eec 100644
--- a/SRC/dgerq2.f
+++ b/SRC/dgerq2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
diff --git a/SRC/dgerqf.f b/SRC/dgerqf.f
index 062638a9..67f1192c 100644
--- a/SRC/dgerqf.f
+++ b/SRC/dgerqf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
diff --git a/SRC/dgetrs.f b/SRC/dgetrs.f
index 927d25cb..89e13dc5 100644
--- a/SRC/dgetrs.f
+++ b/SRC/dgetrs.f
@@ -18,7 +18,7 @@
 *  =======
 *
 *  DGETRS solves a system of linear equations
-*     A * X = B  or  A' * X = B
+*     A * X = B  or  A**T * X = B
 *  with a general N-by-N matrix A using the LU factorization computed
 *  by DGETRF.
 *
@@ -28,8 +28,8 @@
 *  TRANS   (input) CHARACTER*1
 *          Specifies the form of the system of equations:
 *          = 'N':  A * X = B  (No transpose)
-*          = 'T':  A'* X = B  (Transpose)
-*          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
+*          = 'T':  A**T* X = B  (Transpose)
+*          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
 *
 *  N       (input) INTEGER
 *          The order of the matrix A.  N >= 0.
@@ -126,14 +126,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A' * X = B.
+*        Solve A**T * X = B.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B, overwriting B with X.
 *
          CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, overwriting B with X.
 *
          CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE,
      $               A, LDA, B, LDB )
diff --git a/SRC/dggglm.f b/SRC/dggglm.f
index 12a8208b..b75e9af6 100644
--- a/SRC/dggglm.f
+++ b/SRC/dggglm.f
@@ -186,9 +186,9 @@
 *
 *     Compute the GQR factorization of matrices A and B:
 *
-*            Q'*A = ( R11 ) M,    Q'*B*Z' = ( T11   T12 ) M
-*                   (  0  ) N-M             (  0    T22 ) N-M
-*                      M                     M+P-N  N-M
+*          Q**T*A = ( R11 ) M,    Q**T*B*Z**T = ( T11   T12 ) M
+*                   (  0  ) N-M                 (  0    T22 ) N-M
+*                      M                         M+P-N  N-M
 *
 *     where R11 and T22 are upper triangular, and Q and Z are
 *     orthogonal.
@@ -197,8 +197,8 @@
      $             WORK( M+NP+1 ), LWORK-M-NP, INFO )
       LOPT = WORK( M+NP+1 )
 *
-*     Update left-hand-side vector d = Q'*d = ( d1 ) M
-*                                             ( d2 ) N-M
+*     Update left-hand-side vector d = Q**T*d = ( d1 ) M
+*                                               ( d2 ) N-M
 *
       CALL DORMQR( 'Left', 'Transpose', N, 1, M, A, LDA, WORK, D,
      $             MAX( 1, N ), WORK( M+NP+1 ), LWORK-M-NP, INFO )
@@ -245,7 +245,7 @@
          CALL DCOPY( M, D, 1, X, 1 )
       END IF
 *
-*     Backward transformation y = Z'*y
+*     Backward transformation y = Z**T *y
 *
       CALL DORMRQ( 'Left', 'Transpose', P, 1, NP,
      $             B( MAX( 1, N-P+1 ), 1 ), LDB, WORK( M+1 ), Y,
diff --git a/SRC/dgglse.f b/SRC/dgglse.f
index 8b80ddeb..d10c75ad 100644
--- a/SRC/dgglse.f
+++ b/SRC/dgglse.f
@@ -183,9 +183,9 @@
 *
 *     Compute the GRQ factorization of matrices B and A:
 *
-*            B*Q' = (  0  T12 ) P   Z'*A*Q' = ( R11 R12 ) N-P
-*                     N-P  P                  (  0  R22 ) M+P-N
-*                                               N-P  P
+*            B*Q**T = (  0  T12 ) P   Z**T*A*Q**T = ( R11 R12 ) N-P
+*                        N-P  P                     (  0  R22 ) M+P-N
+*                                                      N-P  P
 *
 *     where T12 and R11 are upper triangular, and Q and Z are
 *     orthogonal.
@@ -194,8 +194,8 @@
      $             WORK( P+MN+1 ), LWORK-P-MN, INFO )
       LOPT = WORK( P+MN+1 )
 *
-*     Update c = Z'*c = ( c1 ) N-P
-*                       ( c2 ) M+P-N
+*     Update c = Z**T *c = ( c1 ) N-P
+*                          ( c2 ) M+P-N
 *
       CALL DORMQR( 'Left', 'Transpose', M, 1, MN, A, LDA, WORK( P+1 ),
      $             C, MAX( 1, M ), WORK( P+MN+1 ), LWORK-P-MN, INFO )
@@ -254,7 +254,7 @@
          CALL DAXPY( NR, -ONE, D, 1, C( N-P+1 ), 1 )
       END IF
 *
-*     Backward transformation x = Q'*x
+*     Backward transformation x = Q**T*x
 *
       CALL DORMRQ( 'Left', 'Transpose', N, 1, P, B, LDB, WORK( 1 ), X,
      $             N, WORK( P+MN+1 ), LWORK-P-MN, INFO )
diff --git a/SRC/dggqrf.f b/SRC/dggqrf.f
index edcdb6a7..c4660326 100644
--- a/SRC/dggqrf.f
+++ b/SRC/dggqrf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GQR factorization
 *  of A and B implicitly gives the QR factorization of inv(B)*A:
 *
-*               inv(B)*A = Z'*(inv(T)*R)
+*               inv(B)*A = Z**T*(inv(T)*R)
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
 *  transpose of the matrix Z.
 *
 *  Arguments
@@ -119,7 +119,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**T
 *
 *  where taua is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -133,7 +133,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**T
 *
 *  where taub is a real scalar, and v is a real vector with
 *  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
@@ -194,7 +194,7 @@
       CALL DGEQRF( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := Q'*B.
+*     Update B := Q**T*B.
 *
       CALL DORMQR( 'Left', 'Transpose', N, P, MIN( N, M ), A, LDA, TAUA,
      $             B, LDB, WORK, LWORK, INFO )
diff --git a/SRC/dggrqf.f b/SRC/dggrqf.f
index da8ce675..56d1fc97 100644
--- a/SRC/dggrqf.f
+++ b/SRC/dggrqf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GRQ factorization
 *  of A and B implicitly gives the RQ factorization of A*inv(B):
 *
-*               A*inv(B) = (R*inv(T))*Z'
+*               A*inv(B) = (R*inv(T))*Z**T
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
 *  transpose of the matrix Z.
 *
 *  Arguments
@@ -118,7 +118,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**T
 *
 *  where taua is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
@@ -132,7 +132,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**T
 *
 *  where taub is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
@@ -193,7 +193,7 @@
       CALL DGERQF( M, N, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := B*Q'
+*     Update B := B*Q**T
 *
       CALL DORMRQ( 'Right', 'Transpose', P, N, MIN( M, N ),
      $             A( MAX( 1, M-N+1 ), 1 ), LDA, TAUA, B, LDB, WORK,
diff --git a/SRC/dggsvd.f b/SRC/dggsvd.f
index c03c4ca4..9b5bb017 100644
--- a/SRC/dggsvd.f
+++ b/SRC/dggsvd.f
@@ -24,10 +24,10 @@
 *  DGGSVD computes the generalized singular value decomposition (GSVD)
 *  of an M-by-N real matrix A and P-by-N real matrix B:
 *
-*      U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R )
+*        U**T*A*Q = D1*( 0 R ),    V**T*B*Q = D2*( 0 R )
 *
-*  where U, V and Q are orthogonal matrices, and Z' is the transpose
-*  of Z.  Let K+L = the effective numerical rank of the matrix (A',B')',
+*  where U, V and Q are orthogonal matrices.
+*  Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T,
 *  then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
 *  D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
 *  following structures, respectively:
@@ -86,13 +86,13 @@
 *
 *  In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
 *  A and B implicitly gives the SVD of A*inv(B):
-*                       A*inv(B) = U*(D1*inv(D2))*V'.
-*  If ( A',B')' has orthonormal columns, then the GSVD of A and B is
+*                       A*inv(B) = U*(D1*inv(D2))*V**T.
+*  If ( A**T,B**T)**T  has orthonormal columns, then the GSVD of A and B is
 *  also equal to the CS decomposition of A and B. Furthermore, the GSVD
 *  can be used to derive the solution of the eigenvalue problem:
-*                       A'*A x = lambda* B'*B x.
+*                       A**T*A x = lambda* B**T*B x.
 *  In some literature, the GSVD of A and B is presented in the form
-*                   U'*A*X = ( 0 D1 ),   V'*B*X = ( 0 D2 )
+*                   U**T*A*X = ( 0 D1 ),   V**T*B*X = ( 0 D2 )
 *  where U and V are orthogonal and X is nonsingular, D1 and D2 are
 *  ``diagonal''.  The former GSVD form can be converted to the latter
 *  form by taking the nonsingular matrix X as
@@ -128,7 +128,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in the Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A',B')**T.
 *
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
@@ -209,7 +209,7 @@
 *  TOLA    DOUBLE PRECISION
 *  TOLB    DOUBLE PRECISION
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')'. Generally, they are set to
+*          rank of (A',B')**T. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MAZHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MAZHEPS.
 *          The size of TOLA and TOLB may affect the size of backward
diff --git a/SRC/dggsvp.f b/SRC/dggsvp.f
index 89f1e098..ce717675 100644
--- a/SRC/dggsvp.f
+++ b/SRC/dggsvp.f
@@ -23,24 +23,23 @@
 *
 *  DGGSVP computes orthogonal matrices U, V and Q such that
 *
-*                   N-K-L  K    L
-*   U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
-*                L ( 0     0   A23 )
-*            M-K-L ( 0     0    0  )
+*                     N-K-L  K    L
+*   U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
+*                  L ( 0     0   A23 )
+*              M-K-L ( 0     0    0  )
 *
 *                   N-K-L  K    L
 *          =     K ( 0    A12  A13 )  if M-K-L < 0;
 *              M-K ( 0     0   A23 )
 *
-*                 N-K-L  K    L
-*   V'*B*Q =   L ( 0     0   B13 )
-*            P-L ( 0     0    0  )
+*                   N-K-L  K    L
+*   V**T*B*Q =   L ( 0     0   B13 )
+*              P-L ( 0     0    0  )
 *
 *  where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 *  upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 *  otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
-*  numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the
-*  transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -99,8 +98,8 @@
 *  K       (output) INTEGER
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
-*          described in Purpose.
-*          K + L = effective numerical rank of (A',B')'.
+*          described in Purpose section.
+*          K + L = effective numerical rank of (A**T,B**T)**T.
 *
 *  U       (output) DOUBLE PRECISION array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the orthogonal matrix U.
@@ -258,14 +257,14 @@
 *
          CALL DGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**T
 *
          CALL DORMR2( 'Right', 'Transpose', M, N, L, B, LDB, TAU, A,
      $                LDA, WORK, INFO )
 *
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**T
 *
             CALL DORMR2( 'Right', 'Transpose', N, N, L, B, LDB, TAU, Q,
      $                   LDQ, WORK, INFO )
@@ -287,7 +286,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**T
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -303,7 +302,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL DORM2R( 'Left', 'Transpose', M, L, MIN( M, N-L ), A, LDA,
      $             TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -345,7 +344,7 @@
 *
          IF( WANTQ ) THEN
 *
-*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1'
+*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T
 *
             CALL DORMR2( 'Right', 'Transpose', N, N-L, K, A, LDA, TAU,
      $                   Q, LDQ, WORK, INFO )
diff --git a/SRC/dgtcon.f b/SRC/dgtcon.f
index 330a0c95..f90190ac 100644
--- a/SRC/dgtcon.f
+++ b/SRC/dgtcon.f
@@ -151,7 +151,7 @@
      $                   WORK, N, INFO )
          ELSE
 *
-*           Multiply by inv(L')*inv(U').
+*           Multiply by inv(L**T)*inv(U**T).
 *
             CALL DGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK,
      $                   N, INFO )
diff --git a/SRC/dgtsv.f b/SRC/dgtsv.f
index ab6a9f5d..0d81a248 100644
--- a/SRC/dgtsv.f
+++ b/SRC/dgtsv.f
@@ -22,7 +22,7 @@
 *  where A is an n by n tridiagonal matrix, by Gaussian elimination with
 *  partial pivoting.
 *
-*  Note that the equation  A'*X = B  may be solved by interchanging the
+*  Note that the equation  A**T*X = B  may be solved by interchanging the
 *  order of the arguments DU and DL.
 *
 *  Arguments
diff --git a/SRC/dla_gbamv.f b/SRC/dla_gbamv.f
index c0f246ab..85dc22d0 100644
--- a/SRC/dla_gbamv.f
+++ b/SRC/dla_gbamv.f
@@ -25,7 +25,7 @@
 *  DLA_GBAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -47,43 +47,43 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  KL      (input) INTEGER
+*  KL       (input) INTEGER
 *           The number of subdiagonals within the band of A.  KL >= 0.
 *
-*  KU      (input) INTEGER
+*  KU       (input) INTEGER
 *           The number of superdiagonals within the band of A.  KU >= 0.
 *
-*  ALPHA  - DOUBLE PRECISION
+*  ALPHA    (input) DOUBLE PRECISION
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - DOUBLE PRECISION   array of DIMENSION ( LDA, n )
-*           Before entry, the leading m by n part of the array A must
+*  AB       (input) DOUBLE PRECISION array of DIMENSION ( LDAB, n )
+*           Before entry, the leading m by n part of the array AB must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
-*           On entry, LDA specifies the first dimension of A as declared
-*           in the calling (sub) program. LDA must be at least
+*  LDAB     (input) INTEGER
+*           On entry, LDA specifies the first dimension of AB as declared
+*           in the calling (sub) program. LDAB must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) DOUBLE PRECISION array, dimension
+*  X        (input) DOUBLE PRECISION array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -91,17 +91,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA   - DOUBLE PRECISION
+*  BETA     (input)  DOUBLE PRECISION
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y       (input/output) DOUBLE PRECISION  array, dimension
+*  Y        (input/output) DOUBLE PRECISION  array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -109,7 +109,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
@@ -118,7 +118,7 @@
 *  Level 2 Blas routine.
 *
 *  =====================================================================
-
+*
 *     .. Parameters ..
       DOUBLE PRECISION   ONE, ZERO
       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
diff --git a/SRC/dla_geamv.f b/SRC/dla_geamv.f
index da11197f..37482b4d 100644
--- a/SRC/dla_geamv.f
+++ b/SRC/dla_geamv.f
@@ -25,7 +25,7 @@
 *  DLA_GEAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -47,37 +47,37 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  ALPHA  - DOUBLE PRECISION
+*  ALPHA    (input) DOUBLE PRECISION
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - DOUBLE PRECISION   array of DIMENSION ( LDA, n )
+*  A        (input) DOUBLE PRECISION array of DIMENSION ( LDA, n )
 *           Before entry, the leading m by n part of the array A must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
+*  LDA      (input) INTEGER
 *           On entry, LDA specifies the first dimension of A as declared
 *           in the calling (sub) program. LDA must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) DOUBLE PRECISION array, dimension
+*  X        (input) DOUBLE PRECISION array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -85,17 +85,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA   - DOUBLE PRECISION
+*  BETA     (input) DOUBLE PRECISION
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y      - DOUBLE PRECISION
+*  Y        (input/output) DOUBLE PRECISION
 *           Array of DIMENSION at least
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
@@ -104,7 +104,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/dlabrd.f b/SRC/dlabrd.f
index f48ee892..1793c992 100644
--- a/SRC/dlabrd.f
+++ b/SRC/dlabrd.f
@@ -19,7 +19,7 @@
 *
 *  DLABRD reduces the first NB rows and columns of a real general
 *  m by n matrix A to upper or lower bidiagonal form by an orthogonal
-*  transformation Q' * A * P, and returns the matrices X and Y which
+*  transformation Q**T * A * P, and returns the matrices X and Y which
 *  are needed to apply the transformation to the unreduced part of A.
 *
 *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
@@ -81,14 +81,14 @@
 *          of A.
 *
 *  LDX     (input) INTEGER
-*          The leading dimension of the array X. LDX >= M.
+*          The leading dimension of the array X. LDX >= max(1,M).
 *
 *  Y       (output) DOUBLE PRECISION array, dimension (LDY,NB)
 *          The n-by-nb matrix Y required to update the unreduced part
 *          of A.
 *
 *  LDY     (input) INTEGER
-*          The leading dimension of the array Y. LDY >= N.
+*          The leading dimension of the array Y. LDY >= max(1,N).
 *
 *  Further Details
 *  ===============
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors.
 *
@@ -113,9 +113,9 @@
 *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  The elements of the vectors v and u together form the m-by-nb matrix
-*  V and the nb-by-n matrix U' which are needed, with X and Y, to apply
+*  V and the nb-by-n matrix U**T which are needed, with X and Y, to apply
 *  the transformation to the unreduced part of the matrix, using a block
-*  update of the form:  A := A - V*Y' - X*U'.
+*  update of the form:  A := A - V*Y**T - X*U**T.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with nb = 2:
diff --git a/SRC/dlaed7.f b/SRC/dlaed7.f
index 72a52a43..015942bc 100644
--- a/SRC/dlaed7.f
+++ b/SRC/dlaed7.f
@@ -31,9 +31,9 @@
 *  the case in which all eigenvalues and eigenvectors of a symmetric
 *  tridiagonal matrix are desired.
 *
-*    T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
+*    T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
 *
-*     where Z = Q'u, u is a vector of length N with ones in the
+*     where Z = Q**Tu, u is a vector of length N with ones in the
 *     CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
 *
 *     The eigenvectors of the original matrix are stored in Q, and the
diff --git a/SRC/dlaein.f b/SRC/dlaein.f
index 892df313..991b7f23 100644
--- a/SRC/dlaein.f
+++ b/SRC/dlaein.f
@@ -232,7 +232,7 @@
          DO 110 ITS = 1, N
 *
 *           Solve U*x = scale*v for a right eigenvector
-*             or U'*x = scale*v for a left eigenvector,
+*             or U**T*x = scale*v for a left eigenvector,
 *           overwriting x on v.
 *
             CALL DLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB,
diff --git a/SRC/dlags2.f b/SRC/dlags2.f
index 2e1ccf00..d8541123 100644
--- a/SRC/dlags2.f
+++ b/SRC/dlags2.f
@@ -18,19 +18,19 @@
 *  DLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
 *  that if ( UPPER ) then
 *
-*            U'*A*Q = U'*( A1 A2 )*Q = ( x  0  )
-*                        ( 0  A3 )     ( x  x  )
+*            U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
+*                              ( 0  A3 )     ( x  x  )
 *  and
-*            V'*B*Q = V'*( B1 B2 )*Q = ( x  0  )
-*                        ( 0  B3 )     ( x  x  )
+*            V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
+*                             ( 0  B3 )     ( x  x  )
 *
 *  or if ( .NOT.UPPER ) then
 *
-*            U'*A*Q = U'*( A1 0  )*Q = ( x  x  )
-*                        ( A2 A3 )     ( 0  x  )
+*            U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
+*                              ( A2 A3 )     ( 0  x  )
 *  and
-*            V'*B*Q = V'*( B1 0  )*Q = ( x  x  )
-*                        ( B2 B3 )     ( 0  x  )
+*            V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
+*                            ( B2 B3 )     ( 0  x  )
 *
 *  The rows of the transformed A and B are parallel, where
 *
@@ -112,8 +112,8 @@
          IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
      $        THEN
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11R = CSL*A1
             UA12 = CSL*A2 + SNL*A3
@@ -124,7 +124,7 @@
             AUA12 = ABS( CSL )*ABS( A2 ) + ABS( SNL )*ABS( A3 )
             AVB12 = ABS( CSR )*ABS( B2 ) + ABS( SNR )*ABS( B3 )
 *
-*           zero (1,2) elements of U'*A and V'*B
+*           zero (1,2) elements of U**T *A and V**T *B
 *
             IF( ( ABS( UA11R )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA12 / ( ABS( UA11R )+ABS( UA12 ) ).LE.AVB12 /
@@ -144,8 +144,8 @@
 *
          ELSE
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNL*A1
             UA22 = -SNL*A2 + CSL*A3
@@ -156,7 +156,7 @@
             AUA22 = ABS( SNL )*ABS( A2 ) + ABS( CSL )*ABS( A3 )
             AVB22 = ABS( SNR )*ABS( B2 ) + ABS( CSR )*ABS( B3 )
 *
-*           zero (2,2) elements of U'*A and V'*B, and then swap.
+*           zero (2,2) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA21 )+ABS( UA22 ) ).NE.ZERO ) THEN
                IF( AUA22 / ( ABS( UA21 )+ABS( UA22 ) ).LE.AVB22 /
@@ -197,8 +197,8 @@
          IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) )
      $        THEN
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNR*A1 + CSR*A2
             UA22R = CSR*A3
@@ -209,7 +209,7 @@
             AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS( A2 )
             AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS( B2 )
 *
-*           zero (2,1) elements of U'*A and V'*B.
+*           zero (2,1) elements of U**T *A and V**T *B.
 *
             IF( ( ABS( UA21 )+ABS( UA22R ) ).NE.ZERO ) THEN
                IF( AUA21 / ( ABS( UA21 )+ABS( UA22R ) ).LE.AVB21 /
@@ -229,8 +229,8 @@
 *
          ELSE
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11 = CSR*A1 + SNR*A2
             UA12 = SNR*A3
@@ -241,7 +241,7 @@
             AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS( A2 )
             AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS( B2 )
 *
-*           zero (1,1) elements of U'*A and V'*B, and then swap.
+*           zero (1,1) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA11 )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA11 / ( ABS( UA11 )+ABS( UA12 ) ).LE.AVB11 /
diff --git a/SRC/dlagtm.f b/SRC/dlagtm.f
index 5c8ee6e8..4699e194 100644
--- a/SRC/dlagtm.f
+++ b/SRC/dlagtm.f
@@ -128,7 +128,7 @@
    60       CONTINUE
          ELSE
 *
-*           Compute B := B + A'*X
+*           Compute B := B + A**T*X
 *
             DO 80 J = 1, NRHS
                IF( N.EQ.1 ) THEN
@@ -166,7 +166,7 @@
   100       CONTINUE
          ELSE
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**T*X
 *
             DO 120 J = 1, NRHS
                IF( N.EQ.1 ) THEN
diff --git a/SRC/dlagts.f b/SRC/dlagts.f
index be33157b..c31c7c5d 100644
--- a/SRC/dlagts.f
+++ b/SRC/dlagts.f
@@ -19,7 +19,7 @@
 *
 *  DLAGTS may be used to solve one of the systems of equations
 *
-*     (T - lambda*I)*x = y   or   (T - lambda*I)'*x = y,
+*     (T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,
 *
 *  where T is an n by n tridiagonal matrix, for x, following the
 *  factorization of (T - lambda*I) as
@@ -42,9 +42,9 @@
 *                and, if overflow would otherwise occur, the diagonal
 *                elements of U are to be perturbed. See argument TOL
 *                below.
-*          =  2: The equations  (T - lambda*I)'x = y  are to be solved,
+*          =  2: The equations  (T - lambda*I)**Tx = y  are to be solved,
 *                but diagonal elements of U are not to be perturbed.
-*          = -2: The equations  (T - lambda*I)'x = y  are to be solved
+*          = -2: The equations  (T - lambda*I)**Tx = y  are to be solved
 *                and, if overflow would otherwise occur, the diagonal
 *                elements of U are to be perturbed. See argument TOL
 *                below.
diff --git a/SRC/dlahr2.f b/SRC/dlahr2.f
index c5363d4a..87bf4220 100644
--- a/SRC/dlahr2.f
+++ b/SRC/dlahr2.f
@@ -19,8 +19,8 @@
 *  DLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an orthogonal similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**T * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
 *
 *  This is an auxiliary routine called by DGEHRD.
 *
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -84,7 +84,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**T) * (A - Y*V**T).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -144,12 +144,12 @@
 *
 *           Update A(K+1:N,I)
 *
-*           Update I-th column of A - Y * V'
+*           Update I-th column of A - Y * V**T
 *
             CALL DGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T' * V**T to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -164,13 +164,13 @@
      $                  I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**T * b2
 *
             CALL DGEMV( 'Transpose', N-K-I+1, I-1, 
      $                  ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**T * w
 *
             CALL DTRMV( 'Upper', 'Transpose', 'NON-UNIT', 
      $                  I-1, T, LDT,
diff --git a/SRC/dlahrd.f b/SRC/dlahrd.f
index 2e46e2fb..7fd4736b 100644
--- a/SRC/dlahrd.f
+++ b/SRC/dlahrd.f
@@ -19,8 +19,8 @@
 *  DLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an orthogonal similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**T * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
 *
 *  This is an OBSOLETE auxiliary routine. 
 *  This routine will be 'deprecated' in a  future release.
@@ -76,7 +76,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -85,7 +85,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**T) * (A - Y*V**T).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -130,12 +130,12 @@
 *
 *           Update A(1:n,i)
 *
-*           Compute i-th column of A - Y * V'
+*           Compute i-th column of A - Y * V**T
 *
             CALL DGEMV( 'No transpose', N, I-1, -ONE, Y, LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( 1, I ), 1 )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T**T * V**T to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -143,18 +143,18 @@
 *
 *           where V1 is unit lower triangular
 *
-*           w := V1' * b1
+*           w := V1**T * b1
 *
             CALL DCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
             CALL DTRMV( 'Lower', 'Transpose', 'Unit', I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**T *b2
 *
             CALL DGEMV( 'Transpose', N-K-I+1, I-1, ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**T *w
 *
             CALL DTRMV( 'Upper', 'Transpose', 'Non-unit', I-1, T, LDT,
      $                  T( 1, NB ), 1 )
diff --git a/SRC/dlaic1.f b/SRC/dlaic1.f
index bcd4bd2e..b62a69d6 100644
--- a/SRC/dlaic1.f
+++ b/SRC/dlaic1.f
@@ -40,7 +40,7 @@
 *      diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
 *                                            [ gamma ]
 *
-*  where  alpha =  x'*w.
+*  where  alpha =  x**T*w.
 *
 *  Arguments
 *  =========
diff --git a/SRC/dlaqp2.f b/SRC/dlaqp2.f
index eac307a4..2a677559 100644
--- a/SRC/dlaqp2.f
+++ b/SRC/dlaqp2.f
@@ -133,7 +133,7 @@
 *
          IF( I.LE.N ) THEN
 *
-*           Apply H(i)' to A(offset+i:m,i+1:n) from the left.
+*           Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
 *
             AII = A( OFFPI, I )
             A( OFFPI, I ) = ONE
diff --git a/SRC/dlaqps.f b/SRC/dlaqps.f
index e1ba1221..150b0812 100644
--- a/SRC/dlaqps.f
+++ b/SRC/dlaqps.f
@@ -142,7 +142,7 @@
          END IF
 *
 *        Apply previous Householder reflectors to column K:
-*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
+*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T.
 *
          IF( K.GT.1 ) THEN
             CALL DGEMV( 'No transpose', M-RK+1, K-1, -ONE, A( RK, 1 ),
@@ -162,7 +162,7 @@
 *
 *        Compute Kth column of F:
 *
-*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
+*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K).
 *
          IF( K.LT.N ) THEN
             CALL DGEMV( 'Transpose', M-RK+1, N-K, TAU( K ),
@@ -177,7 +177,7 @@
    20    CONTINUE
 *
 *        Incremental updating of F:
-*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
+*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T
 *                    *A(RK:M,K).
 *
          IF( K.GT.1 ) THEN
@@ -189,7 +189,7 @@
          END IF
 *
 *        Update the current row of A:
-*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
+*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T.
 *
          IF( K.LT.N ) THEN
             CALL DGEMV( 'No transpose', N-K, K, -ONE, F( K+1, 1 ), LDF,
@@ -229,7 +229,7 @@
 *
 *     Apply the block reflector to the rest of the matrix:
 *     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
-*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
+*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T.
 *
       IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
          CALL DGEMM( 'No transpose', 'Transpose', M-RK, N-KB, KB, -ONE,
diff --git a/SRC/dlaqsb.f b/SRC/dlaqsb.f
index a57db191..84eb9f41 100644
--- a/SRC/dlaqsb.f
+++ b/SRC/dlaqsb.f
@@ -45,7 +45,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T*U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/dlaqtr.f b/SRC/dlaqtr.f
index e56a1c23..18c42f46 100644
--- a/SRC/dlaqtr.f
+++ b/SRC/dlaqtr.f
@@ -51,7 +51,7 @@
 *  LTRAN   (input) LOGICAL
 *          On entry, LTRAN specifies the option of conjugate transpose:
 *             = .FALSE.,    op(T+i*B) = T+i*B,
-*             = .TRUE.,     op(T+i*B) = (T+i*B)'.
+*             = .TRUE.,     op(T+i*B) = (T+i*B)**T.
 *
 *  LREAL   (input) LOGICAL
 *          On entry, LREAL specifies the input matrix structure:
@@ -532,7 +532,7 @@
 *
          ELSE
 *
-*           Solve (T + iB)'*(p+iq) = c+id
+*           Solve (T + iB)**T*(p+iq) = c+id
 *
             JNEXT = 1
             DO 80 J = 1, N
diff --git a/SRC/dlar1v.f b/SRC/dlar1v.f
index 7dfaabfe..43d6f5e8 100644
--- a/SRC/dlar1v.f
+++ b/SRC/dlar1v.f
@@ -25,14 +25,14 @@
 *
 *  DLAR1V computes the (scaled) r-th column of the inverse of
 *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix
-*  L D L^T - sigma I. When sigma is close to an eigenvalue, the
+*  L D L**T - sigma I. When sigma is close to an eigenvalue, the
 *  computed vector is an accurate eigenvector. Usually, r corresponds
 *  to the index where the eigenvector is largest in magnitude.
 *  The following steps accomplish this computation :
-*  (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T,
-*  (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T,
+*  (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
+*  (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
 *  (c) Computation of the diagonal elements of the inverse of
-*      L D L^T - sigma I by combining the above transforms, and choosing
+*      L D L**T - sigma I by combining the above transforms, and choosing
 *      r as the index where the diagonal of the inverse is (one of the)
 *      largest in magnitude.
 *  (d) Computation of the (scaled) r-th column of the inverse using the
@@ -43,18 +43,18 @@
 *  =========
 *
 *  N        (input) INTEGER
-*           The order of the matrix L D L^T.
+*           The order of the matrix L D L**T.
 *
 *  B1       (input) INTEGER
-*           First index of the submatrix of L D L^T.
+*           First index of the submatrix of L D L**T.
 *
 *  BN       (input) INTEGER
-*           Last index of the submatrix of L D L^T.
+*           Last index of the submatrix of L D L**T.
 *
 *  LAMBDA    (input) DOUBLE PRECISION
 *           The shift. In order to compute an accurate eigenvector,
 *           LAMBDA should be a good approximation to an eigenvalue
-*           of L D L^T.
+*           of L D L**T.
 *
 *  L        (input) DOUBLE PRECISION array, dimension (N-1)
 *           The (n-1) subdiagonal elements of the unit bidiagonal matrix
@@ -86,20 +86,20 @@
 *
 *  NEGCNT   (output) INTEGER
 *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
-*           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.
+*           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.
 *
 *  ZTZ      (output) DOUBLE PRECISION
 *           The square of the 2-norm of Z.
 *
 *  MINGMA   (output) DOUBLE PRECISION
 *           The reciprocal of the largest (in magnitude) diagonal
-*           element of the inverse of L D L^T - sigma I.
+*           element of the inverse of L D L**T - sigma I.
 *
 *  R        (input/output) INTEGER
 *           The twist index for the twisted factorization used to
 *           compute Z.
 *           On input, 0 <= R <= N. If R is input as 0, R is set to
-*           the index where (L D L^T - sigma I)^{-1} is largest
+*           the index where (L D L**T - sigma I)^{-1} is largest
 *           in magnitude. If 1 <= R <= N, R is unchanged.
 *           On output, R contains the twist index used to compute Z.
 *           Ideally, R designates the position of the maximum entry in the
diff --git a/SRC/dlarf.f b/SRC/dlarf.f
index 2223d71b..ebc6877d 100644
--- a/SRC/dlarf.f
+++ b/SRC/dlarf.f
@@ -21,7 +21,7 @@
 *  DLARF applies a real elementary reflector H to a real m by n matrix
 *  C, from either the left or the right. H is represented in the form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
@@ -121,12 +121,12 @@
 *
          IF( LASTV.GT.0 ) THEN
 *
-*           w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)
+*           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
 *
             CALL DGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
      $           ZERO, WORK, 1 )
 *
-*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'
+*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
 *
             CALL DGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
          END IF
@@ -141,7 +141,7 @@
             CALL DGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
      $           V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'
+*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
 *
             CALL DGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
          END IF
diff --git a/SRC/dlarfb.f b/SRC/dlarfb.f
index 3c5cb4eb..024a0b46 100644
--- a/SRC/dlarfb.f
+++ b/SRC/dlarfb.f
@@ -19,19 +19,19 @@
 *  Purpose
 *  =======
 *
-*  DLARFB applies a real block reflector H or its transpose H' to a
+*  DLARFB applies a real block reflector H or its transpose H**T to a
 *  real m by n matrix C, from either the left or the right.
 *
 *  Arguments
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**T from the Left
+*          = 'R': apply H or H**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'T': apply H' (Transpose)
+*          = 'T': apply H**T (Transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -76,10 +76,10 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
 *
 *  LDC     (input) INTEGER
-*          The leading dimension of the array C. LDA >= max(1,M).
+*          The leading dimension of the array C. LDC >= max(1,M).
 *
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (LDWORK,K)
 *
@@ -154,15 +154,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
                LASTC = ILADLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
-*              W := C1'
+*              W := C1**T
 *
                DO 10 J = 1, K
                   CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
@@ -174,7 +174,7 @@
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2
+*                 W := W + C2**T *V2
 *
                   CALL DGEMM( 'Transpose', 'No transpose',
      $                 LASTC, K, LASTV-K,
@@ -182,16 +182,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2 * W'
+*                 C2 := C2 - V2 * W**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTV-K, LASTC, K,
@@ -199,12 +199,12 @@
      $                 C( K+1, 1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**T
 *
                DO 30 J = 1, K
                   DO 20 I = 1, LASTC
@@ -214,7 +214,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
                LASTC = ILADLR( M, LASTV, C, LDC )
@@ -241,16 +241,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - W * V2'
+*                 C2 := C2 - W * V2**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTC, LASTV-K, K,
@@ -258,7 +258,7 @@
      $                 C( 1, K+1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
@@ -280,15 +280,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILADLR( M, K, V, LDV ) )
                LASTC = ILADLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C' * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
-*              W := C2'
+*              W := C2**T
 *
                DO 70 J = 1, K
                   CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -302,36 +302,36 @@
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1
+*                 W := W + C1**T*V1
 *
                   CALL DGEMM( 'Transpose', 'No transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1 * W'
+*                 C1 := C1 - V1 * W**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**T
 *
                DO 90 J = 1, K
                   DO 80 I = 1, LASTC
@@ -341,7 +341,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILADLR( N, K, V, LDV ) )
                LASTC = ILADLR( M, LASTV, C, LDC )
@@ -368,7 +368,7 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -377,14 +377,14 @@
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - W * V1'
+*                 C1 := C1 - W * V1**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
@@ -409,27 +409,27 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
                LASTC = ILADLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
-*              W := C1'
+*              W := C1**T
 *
                DO 130 J = 1, K
                   CALL DCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
   130          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2'
+*                 W := W + C2**T*V2**T
 *
                   CALL DGEMM( 'Transpose', 'Transpose',
      $                 LASTC, K, LASTV-K,
@@ -437,16 +437,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL DTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**T * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2' * W'
+*                 C2 := C2 - V2**T * W**T
 *
                   CALL DGEMM( 'Transpose', 'Transpose',
      $                 LASTV-K, LASTC, K,
@@ -459,7 +459,7 @@
                CALL DTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**T
 *
                DO 150 J = 1, K
                   DO 140 I = 1, LASTC
@@ -469,12 +469,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
                LASTC = ILADLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C1
 *
@@ -482,13 +482,13 @@
                   CALL DCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL DTRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2 * V2'
+*                 W := W + C2 * V2**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTC, K, LASTV-K,
@@ -496,7 +496,7 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL DTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -535,45 +535,45 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILADLC( K, M, V, LDV ) )
                LASTC = ILADLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
-*              W := C2'
+*              W := C2**T
 *
                DO 190 J = 1, K
                   CALL DCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
      $                 WORK( 1, J ), 1 )
   190          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1'
+*                 W := W + C1**T * V1**T
 *
                   CALL DGEMM( 'Transpose', 'Transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**T * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1' * W'
+*                 C1 := C1 - V1**T * W**T
 *
                   CALL DGEMM( 'Transpose', 'Transpose',
      $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
@@ -586,7 +586,7 @@
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**T
 *
                DO 210 J = 1, K
                   DO 200 I = 1, LASTC
@@ -596,12 +596,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILADLC( K, N, V, LDV ) )
                LASTC = ILADLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C2
 *
@@ -610,21 +610,21 @@
      $                 WORK( 1, J ), 1 )
   220          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL DTRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1 * V1'
+*                 W := W + C1 * V1**T
 *
                   CALL DGEMM( 'No transpose', 'Transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
diff --git a/SRC/dlarfg.f b/SRC/dlarfg.f
index 36e5d89e..e8190d51 100644
--- a/SRC/dlarfg.f
+++ b/SRC/dlarfg.f
@@ -19,13 +19,13 @@
 *  DLARFG generates a real elementary reflector H of order n, such
 *  that
 *
-*        H * ( alpha ) = ( beta ),   H' * H = I.
+*        H * ( alpha ) = ( beta ),   H**T * H = I.
 *            (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, and x is an (n-1)-element real
 *  vector. H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**T ) ,
 *                      ( v )
 *
 *  where tau is a real scalar and v is a real (n-1)-element
diff --git a/SRC/dlarfgp.f b/SRC/dlarfgp.f
index e65bf47d..3c5819f6 100644
--- a/SRC/dlarfgp.f
+++ b/SRC/dlarfgp.f
@@ -19,13 +19,13 @@
 *  DLARFGP generates a real elementary reflector H of order n, such
 *  that
 *
-*        H * ( alpha ) = ( beta ),   H' * H = I.
+*        H * ( alpha ) = ( beta ),   H**T * H = I.
 *            (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, beta is non-negative, and x is
 *  an (n-1)-element real vector.  H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**T ) ,
 *                      ( v )
 *
 *  where tau is a real scalar and v is a real (n-1)-element
diff --git a/SRC/dlarft.f b/SRC/dlarft.f
index 9b05e869..fde95a06 100644
--- a/SRC/dlarft.f
+++ b/SRC/dlarft.f
@@ -27,12 +27,12 @@
 *  If STOREV = 'C', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th column of the array V, and
 *
-*     H  =  I - V * T * V'
+*     H  =  I - V * T * V**T
 *
 *  If STOREV = 'R', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th row of the array V, and
 *
-*     H  =  I - V' * T * V
+*     H  =  I - V**T * T * V
 *
 *  Arguments
 *  =========
@@ -150,7 +150,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i)
+*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
 *
                   CALL DGEMV( 'Transpose', J-I+1, I-1, -TAU( I ),
      $                        V( I, 1 ), LDV, V( I, I ), 1, ZERO,
@@ -162,7 +162,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)'
+*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
 *
                   CALL DGEMV( 'No transpose', I-1, J-I+1, -TAU( I ),
      $                        V( 1, I ), LDV, V( I, I ), LDV, ZERO,
@@ -207,7 +207,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i)
+*                            - tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
 *
                      CALL DGEMV( 'Transpose', N-K+I-J+1, K-I, -TAU( I ),
      $                           V( J, I+1 ), LDV, V( J, I ), 1, ZERO,
@@ -223,7 +223,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)'
+*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
 *
                      CALL DGEMV( 'No transpose', K-I, N-K+I-J+1,
      $                    -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
diff --git a/SRC/dlarfx.f b/SRC/dlarfx.f
index 6f056e13..24a02587 100644
--- a/SRC/dlarfx.f
+++ b/SRC/dlarfx.f
@@ -22,7 +22,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
diff --git a/SRC/dlarrv.f b/SRC/dlarrv.f
index 8adcd24f..e5bd2172 100644
--- a/SRC/dlarrv.f
+++ b/SRC/dlarrv.f
@@ -25,7 +25,7 @@
 *  =======
 *
 *  DLARRV computes the eigenvectors of the tridiagonal matrix
-*  T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T.
+*  T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
 *  The input eigenvalues should have been computed by DLARRE.
 *
 *  Arguments
diff --git a/SRC/dlarz.f b/SRC/dlarz.f
index 1b6570fa..0200d893 100644
--- a/SRC/dlarz.f
+++ b/SRC/dlarz.f
@@ -21,7 +21,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
@@ -101,7 +101,7 @@
 *
             CALL DCOPY( N, C, LDC, WORK, 1 )
 *
-*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
+*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
 *
             CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
      $                  INCV, ONE, WORK, 1 )
@@ -111,7 +111,7 @@
             CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
 *
 *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                               tau * v( 1:l ) * w( 1:n )'
+*                               tau * v( 1:l ) * w( 1:n )**T
 *
             CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
      $                 LDC )
@@ -137,7 +137,7 @@
             CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
 *
 *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
-*                               tau * w( 1:m ) * v( 1:l )'
+*                               tau * w( 1:m ) * v( 1:l )**T
 *
             CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
      $                 LDC )
diff --git a/SRC/dlarzb.f b/SRC/dlarzb.f
index 9fc839d4..fbe5a9a0 100644
--- a/SRC/dlarzb.f
+++ b/SRC/dlarzb.f
@@ -27,12 +27,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**T from the Left
+*          = 'R': apply H or H**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Transpose)
+*          = 'C': apply H**T (Transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -77,7 +77,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -140,16 +140,16 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        Form  H * C  or  H' * C
+*        Form  H * C  or  H**T * C
 *
-*        W( 1:n, 1:k ) = C( 1:k, 1:n )'
+*        W( 1:n, 1:k ) = C( 1:k, 1:n )**T
 *
          DO 10 J = 1, K
             CALL DCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10    CONTINUE
 *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
-*                        C( m-l+1:m, 1:n )' * V( 1:k, 1:l )'
+*                        C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
@@ -160,7 +160,7 @@
          CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
      $               LDT, WORK, LDWORK )
 *
-*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )'
+*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
 *
          DO 30 J = 1, N
             DO 20 I = 1, K
@@ -169,7 +169,7 @@
    30    CONTINUE
 *
 *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                            V( 1:k, 1:l )' * W( 1:n, 1:k )'
+*                            V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
 *
          IF( L.GT.0 )
      $      CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
@@ -177,7 +177,7 @@
 *
       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*        Form  C * H  or  C * H'
+*        Form  C * H  or  C * H**T
 *
 *        W( 1:m, 1:k ) = C( 1:m, 1:k )
 *
@@ -186,13 +186,13 @@
    40    CONTINUE
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
-*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )'
+*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
      $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *
-*        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T'
+*        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T**T
 *
          CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
      $               LDT, WORK, LDWORK )
diff --git a/SRC/dlarzt.f b/SRC/dlarzt.f
index 0f734754..dbbe29c7 100644
--- a/SRC/dlarzt.f
+++ b/SRC/dlarzt.f
@@ -164,7 +164,7 @@
 *
             IF( I.LT.K ) THEN
 *
-*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
+*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
 *
                CALL DGEMV( 'No transpose', K-I, N, -TAU( I ),
      $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
diff --git a/SRC/dlasd1.f b/SRC/dlasd1.f
index f13a2abc..797cc0c0 100644
--- a/SRC/dlasd1.f
+++ b/SRC/dlasd1.f
@@ -98,8 +98,8 @@
 *
 *  VT     (input/output) DOUBLE PRECISION array, dimension(LDVT,M)
 *         where M = N + SQRE.
-*         On entry VT(1:NL+1, 1:NL+1)' contains the right singular
-*         vectors of the upper block; VT(NL+2:M, NL+2:M)' contains
+*         On entry VT(1:NL+1, 1:NL+1)**T contains the right singular
+*         vectors of the upper block; VT(NL+2:M, NL+2:M)**T contains
 *         the right singular vectors of the lower block. On exit
 *         VT' contains the right singular vectors of the
 *         bidiagonal matrix.
diff --git a/SRC/dlasyf.f b/SRC/dlasyf.f
index 0e817cbf..cd69b1e0 100644
--- a/SRC/dlasyf.f
+++ b/SRC/dlasyf.f
@@ -21,11 +21,11 @@
 *  using the Bunch-Kaufman diagonal pivoting method. The partial
 *  factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
 *
-*  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) (  0  A22 ) (  0    I   )
+*  A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
+*        ( L21  I ) (  0  A22 ) (  0       I    )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
@@ -313,7 +313,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
 *
 *        computing blocks of NB columns at a time
 *
@@ -536,7 +536,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
 *
 *        computing blocks of NB columns at a time
 *
diff --git a/SRC/dlatrd.f b/SRC/dlatrd.f
index 1b5b603a..0c39a824 100644
--- a/SRC/dlatrd.f
+++ b/SRC/dlatrd.f
@@ -18,7 +18,7 @@
 *
 *  DLATRD reduces NB rows and columns of a real symmetric matrix A to
 *  symmetric tridiagonal form by an orthogonal similarity
-*  transformation Q' * A * Q, and returns the matrices V and W which are
+*  transformation Q**T * A * Q, and returns the matrices V and W which are
 *  needed to apply the transformation to the unreduced part of A.
 *
 *  If UPLO = 'U', DLATRD reduces the last NB rows and columns of a
@@ -95,7 +95,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
@@ -108,7 +108,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -117,7 +117,7 @@
 *  The elements of the vectors v together form the n-by-nb matrix V
 *  which is needed, with W, to apply the transformation to the unreduced
 *  part of the matrix, using a symmetric rank-2k update of the form:
-*  A := A - V*W' - W*V'.
+*  A := A - V*W**T - W*V**T.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with n = 5 and nb = 2:
diff --git a/SRC/dlatrz.f b/SRC/dlatrz.f
index 07e581b9..2fac6e8f 100644
--- a/SRC/dlatrz.f
+++ b/SRC/dlatrz.f
@@ -64,7 +64,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/dlatzm.f b/SRC/dlatzm.f
index 2d735fe3..f7a688ff 100644
--- a/SRC/dlatzm.f
+++ b/SRC/dlatzm.f
@@ -21,8 +21,8 @@
 *
 *  DLATZM applies a Householder matrix generated by DTZRQF to a matrix.
 *
-*  Let P = I - tau*u*u',   u = ( 1 ),
-*                              ( v )
+*  Let P = I - tau*u*u**T,   u = ( 1 ),
+*                                ( v )
 *  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
 *  SIDE = 'R'.
 *
@@ -110,13 +110,13 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        w := C1 + v' * C2
+*        w :=  (C1 + v**T * C2)**T
 *
          CALL DCOPY( N, C1, LDC, WORK, 1 )
          CALL DGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
+*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
 *        [ C2 ]    [ C2 ]        [ v ]
 *
          CALL DAXPY( N, -TAU, WORK, 1, C1, LDC )
@@ -130,7 +130,7 @@
          CALL DGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
+*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
 *
          CALL DAXPY( M, -TAU, WORK, 1, C1, 1 )
          CALL DGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
diff --git a/SRC/dlauu2.f b/SRC/dlauu2.f
index 77bda092..1e6bdfec 100644
--- a/SRC/dlauu2.f
+++ b/SRC/dlauu2.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  DLAUU2 computes the product U * U' or L' * L, where the triangular
+*  DLAUU2 computes the product U * U**T or L**T * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**T;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**T * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -100,7 +100,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product U * U'.
+*        Compute the product U * U**T.
 *
          DO 10 I = 1, N
             AII = A( I, I )
@@ -115,7 +115,7 @@
 *
       ELSE
 *
-*        Compute the product L' * L.
+*        Compute the product L**T * L.
 *
          DO 20 I = 1, N
             AII = A( I, I )
diff --git a/SRC/dlauum.f b/SRC/dlauum.f
index 21734b79..fb9fdb5f 100644
--- a/SRC/dlauum.f
+++ b/SRC/dlauum.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  DLAUUM computes the product U * U' or L' * L, where the triangular
+*  DLAUUM computes the product U * U**T or L**T * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**T;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**T * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -112,7 +112,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the product U * U'.
+*           Compute the product U * U**T.
 *
             DO 10 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
@@ -131,7 +131,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute the product L' * L.
+*           Compute the product L**T * L.
 *
             DO 20 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
diff --git a/SRC/dorglq.f b/SRC/dorglq.f
index abe409c3..eb83f24f 100644
--- a/SRC/dorglq.f
+++ b/SRC/dorglq.f
@@ -185,7 +185,7 @@
                CALL DLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
      $                      LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i+ib:m,i:n) from the right
+*              Apply H**T to A(i+ib:m,i:n) from the right
 *
                CALL DLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise',
      $                      M-I-IB+1, N-I+1, IB, A( I, I ), LDA, WORK,
@@ -193,7 +193,7 @@
      $                      LDWORK )
             END IF
 *
-*           Apply H' to columns i:n of current block
+*           Apply H**T to columns i:n of current block
 *
             CALL DORGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
      $                   IINFO )
diff --git a/SRC/dorgrq.f b/SRC/dorgrq.f
index c2e0a916..b4499c87 100644
--- a/SRC/dorgrq.f
+++ b/SRC/dorgrq.f
@@ -193,14 +193,14 @@
                CALL DLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
      $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
+*              Apply H**T to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
 *
                CALL DLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise',
      $                      II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK,
      $                      LDWORK, A, LDA, WORK( IB+1 ), LDWORK )
             END IF
 *
-*           Apply H' to columns 1:n-k+i+ib-1 of current block
+*           Apply H**T to columns 1:n-k+i+ib-1 of current block
 *
             CALL DORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
      $                   WORK, IINFO )
diff --git a/SRC/dorm2l.f b/SRC/dorm2l.f
index 27489cbe..ac1990a3 100644
--- a/SRC/dorm2l.f
+++ b/SRC/dorm2l.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T * C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/dorm2r.f b/SRC/dorm2r.f
index 9959c330..6e847452 100644
--- a/SRC/dorm2r.f
+++ b/SRC/dorm2r.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/dorml2.f b/SRC/dorml2.f
index dca1bc8f..ab784bbc 100644
--- a/SRC/dorml2.f
+++ b/SRC/dorml2.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/dormlq.f b/SRC/dormlq.f
index aa1b8391..edb381fd 100644
--- a/SRC/dormlq.f
+++ b/SRC/dormlq.f
@@ -241,19 +241,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL DLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
diff --git a/SRC/dormql.f b/SRC/dormql.f
index 29affb67..f4e9dcff 100644
--- a/SRC/dormql.f
+++ b/SRC/dormql.f
@@ -237,17 +237,17 @@
      $                   A( 1, I ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL DLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
      $                   IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/dormqr.f b/SRC/dormqr.f
index 1cf67e12..5cc54e19 100644
--- a/SRC/dormqr.f
+++ b/SRC/dormqr.f
@@ -234,19 +234,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL DLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
      $                   IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
diff --git a/SRC/dormr2.f b/SRC/dormr2.f
index 9a8ce03d..8c1fcae7 100644
--- a/SRC/dormr2.f
+++ b/SRC/dormr2.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,8 +39,8 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/dormr3.f b/SRC/dormr3.f
index 94b960fa..cf33553e 100644
--- a/SRC/dormr3.f
+++ b/SRC/dormr3.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -80,7 +80,7 @@
 *
 *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -181,19 +181,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**T is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**T is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**T
 *
          CALL DLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
      $               C( IC, JC ), LDC, WORK )
diff --git a/SRC/dormrq.f b/SRC/dormrq.f
index 097a1a02..07d54b80 100644
--- a/SRC/dormrq.f
+++ b/SRC/dormrq.f
@@ -244,17 +244,17 @@
      $                   A( I, 1 ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL DLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/dormrz.f b/SRC/dormrz.f
index b9f775ac..a6c5f2aa 100644
--- a/SRC/dormrz.f
+++ b/SRC/dormrz.f
@@ -264,19 +264,19 @@
 *
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL DLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
diff --git a/SRC/dpbcon.f b/SRC/dpbcon.f
index e474b6a9..297cc2af 100644
--- a/SRC/dpbcon.f
+++ b/SRC/dpbcon.f
@@ -139,7 +139,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL DLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
@@ -160,7 +160,7 @@
      $                   INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL DLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
diff --git a/SRC/dpbsv.f b/SRC/dpbsv.f
index 0095f564..e4a89bcc 100644
--- a/SRC/dpbsv.f
+++ b/SRC/dpbsv.f
@@ -135,7 +135,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dpbsvx.f b/SRC/dpbsvx.f
index 6469b1e8..4986097b 100644
--- a/SRC/dpbsvx.f
+++ b/SRC/dpbsvx.f
@@ -352,7 +352,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T *U or A = L*L**T.
 *
          IF( UPPER ) THEN
             DO 40 J = 1, N
diff --git a/SRC/dpbtf2.f b/SRC/dpbtf2.f
index 1b6b1bf1..2296f8bf 100644
--- a/SRC/dpbtf2.f
+++ b/SRC/dpbtf2.f
@@ -20,9 +20,9 @@
 *  positive definite band matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
-*  where U is an upper triangular matrix, U' is the transpose of U, and
+*     A = U**T * U ,  if UPLO = 'U', or
+*     A = L  * L**T,  if UPLO = 'L',
+*  where U is an upper triangular matrix, U**T is the transpose of U, and
 *  L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -52,7 +52,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T*U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
@@ -137,7 +137,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T*U.
 *
          DO 10 J = 1, N
 *
@@ -161,7 +161,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/dpbtrs.f b/SRC/dpbtrs.f
index 951df583..eb1dcd72 100644
--- a/SRC/dpbtrs.f
+++ b/SRC/dpbtrs.f
@@ -107,11 +107,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T *U.
 *
          DO 10 J = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**T *X = B, overwriting B with X.
 *
             CALL DTBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
@@ -123,7 +123,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**T.
 *
          DO 20 J = 1, NRHS
 *
@@ -132,7 +132,7 @@
             CALL DTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
 *
-*           Solve L'*X = B, overwriting B with X.
+*           Solve L**T *X = B, overwriting B with X.
 *
             CALL DTBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
diff --git a/SRC/dpocon.f b/SRC/dpocon.f
index 6456e600..6e6a1085 100644
--- a/SRC/dpocon.f
+++ b/SRC/dpocon.f
@@ -129,7 +129,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL DLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
@@ -147,7 +147,7 @@
      $                   A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL DLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
diff --git a/SRC/dposv.f b/SRC/dposv.f
index 57a4682a..c93b9fd6 100644
--- a/SRC/dposv.f
+++ b/SRC/dposv.f
@@ -105,7 +105,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL DPOTRF( UPLO, N, A, LDA, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dposvx.f b/SRC/dposvx.f
index c2744f7d..a9ce9272 100644
--- a/SRC/dposvx.f
+++ b/SRC/dposvx.f
@@ -320,7 +320,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T *U or A = L*L**T.
 *
          CALL DLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL DPOTRF( UPLO, N, AF, LDAF, INFO )
diff --git a/SRC/dpotf2.f b/SRC/dpotf2.f
index feaa553a..6c7adae8 100644
--- a/SRC/dpotf2.f
+++ b/SRC/dpotf2.f
@@ -20,8 +20,8 @@
 *  positive definite matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
+*     A = U**T * U ,  if UPLO = 'U', or
+*     A = L  * L**T,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -48,7 +48,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U'*U  or A = L*L'.
+*          factorization A = U**T *U  or A = L*L**T.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T *U.
 *
          DO 10 J = 1, N
 *
@@ -131,7 +131,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/dpotrf.f b/SRC/dpotrf.f
index 271e929c..e3d7bafa 100644
--- a/SRC/dpotrf.f
+++ b/SRC/dpotrf.f
@@ -116,7 +116,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the Cholesky factorization A = U'*U.
+*           Compute the Cholesky factorization A = U**T*U.
 *
             DO 10 J = 1, N, NB
 *
@@ -144,7 +144,7 @@
 *
          ELSE
 *
-*           Compute the Cholesky factorization A = L*L'.
+*           Compute the Cholesky factorization A = L*L**T.
 *
             DO 20 J = 1, N, NB
 *
diff --git a/SRC/dpotri.f b/SRC/dpotri.f
index b3d0eb44..e0c7a75d 100644
--- a/SRC/dpotri.f
+++ b/SRC/dpotri.f
@@ -86,7 +86,7 @@
       IF( INFO.GT.0 )
      $   RETURN
 *
-*     Form inv(U)*inv(U)' or inv(L)'*inv(L).
+*     Form inv(U) * inv(U)**T or inv(L)**T * inv(L).
 *
       CALL DLAUUM( UPLO, N, A, LDA, INFO )
 *
diff --git a/SRC/dpotrs.f b/SRC/dpotrs.f
index 7b199d0e..6851fea2 100644
--- a/SRC/dpotrs.f
+++ b/SRC/dpotrs.f
@@ -100,9 +100,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T *U.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B, overwriting B with X.
 *
          CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
@@ -113,14 +113,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**T.
 *
 *        Solve L*X = B, overwriting B with X.
 *
          CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
      $               NRHS, ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, overwriting B with X.
 *
          CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
diff --git a/SRC/dppcon.f b/SRC/dppcon.f
index c0040aff..239fd8da 100644
--- a/SRC/dppcon.f
+++ b/SRC/dppcon.f
@@ -128,7 +128,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL DLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
@@ -146,7 +146,7 @@
      $                   AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL DLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
      $                   AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
diff --git a/SRC/dppsv.f b/SRC/dppsv.f
index 6eb40e21..a8a5fe8d 100644
--- a/SRC/dppsv.f
+++ b/SRC/dppsv.f
@@ -117,7 +117,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL DPPTRF( UPLO, N, AP, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dppsvx.f b/SRC/dppsvx.f
index cb0cf4e7..76051de0 100644
--- a/SRC/dppsvx.f
+++ b/SRC/dppsvx.f
@@ -112,17 +112,18 @@
 *                            (N*(N+1)/2)
 *          If FACT = 'F', then AFP is an input argument and on entry
 *          contains the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L', in the same storage
+*          factorization A = U**T*U or A = L*L**T, in the same storage
 *          format as A.  If EQUED .ne. 'N', then AFP is the factored
 *          form of the equilibrated matrix A.
 *
 *          If FACT = 'N', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L' of the original matrix A.
+*          factorization A = U**T * U or A = L * L**T of the original
+*          matrix A.
 *
 *          If FACT = 'E', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L' of the equilibrated
+*          factorization A = U**T * U or A = L * L**T of the equilibrated
 *          matrix A (see the description of AP for the form of the
 *          equilibrated matrix).
 *
@@ -324,7 +325,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T * U or A = L * L**T.
 *
          CALL DCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL DPPTRF( UPLO, N, AFP, INFO )
diff --git a/SRC/dpptrf.f b/SRC/dpptrf.f
index 8efaa34a..99648e43 100644
--- a/SRC/dpptrf.f
+++ b/SRC/dpptrf.f
@@ -115,7 +115,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T*U.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -139,7 +139,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/dpptri.f b/SRC/dpptri.f
index 80a33f39..b5a317e3 100644
--- a/SRC/dpptri.f
+++ b/SRC/dpptri.f
@@ -95,7 +95,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product inv(U) * inv(U)'.
+*        Compute the product inv(U) * inv(U)**T.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -109,7 +109,7 @@
 *
       ELSE
 *
-*        Compute the product inv(L)' * inv(L).
+*        Compute the product inv(L)**T * inv(L).
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/dpptrs.f b/SRC/dpptrs.f
index d3e93a05..de90cfaa 100644
--- a/SRC/dpptrs.f
+++ b/SRC/dpptrs.f
@@ -96,11 +96,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T * U.
 *
          DO 10 I = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**T *X = B, overwriting B with X.
 *
             CALL DTPSV( 'Upper', 'Transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
@@ -112,7 +112,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L * L**T.
 *
          DO 20 I = 1, NRHS
 *
@@ -121,7 +121,7 @@
             CALL DTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
 *
-*           Solve L'*X = Y, overwriting B with X.
+*           Solve L**T *X = Y, overwriting B with X.
 *
             CALL DTPSV( 'Lower', 'Transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
diff --git a/SRC/dptcon.f b/SRC/dptcon.f
index 2b9979cf..a0d162c2 100644
--- a/SRC/dptcon.f
+++ b/SRC/dptcon.f
@@ -117,7 +117,7 @@
 *        m(i,j) =  abs(A(i,j)), i = j,
 *        m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**T.
 *
 *     Solve M(L) * x = e.
 *
@@ -126,7 +126,7 @@
          WORK( I ) = ONE + WORK( I-1 )*ABS( E( I-1 ) )
    20 CONTINUE
 *
-*     Solve D * M(L)' * x = b.
+*     Solve D * M(L)**T * x = b.
 *
       WORK( N ) = WORK( N ) / D( N )
       DO 30 I = N - 1, 1, -1
diff --git a/SRC/dptrfs.f b/SRC/dptrfs.f
index a1d822db..2f7dfd93 100644
--- a/SRC/dptrfs.f
+++ b/SRC/dptrfs.f
@@ -263,7 +263,7 @@
 *           m(i,j) =  abs(A(i,j)), i = j,
 *           m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**T.
 *
 *        Solve M(L) * x = e.
 *
@@ -272,7 +272,7 @@
             WORK( I ) = ONE + WORK( I-1 )*ABS( EF( I-1 ) )
    60    CONTINUE
 *
-*        Solve D * M(L)' * x = b.
+*        Solve D * M(L)**T * x = b.
 *
          WORK( N ) = WORK( N ) / DF( N )
          DO 70 I = N - 1, 1, -1
diff --git a/SRC/dptsv.f b/SRC/dptsv.f
index a7e0a282..c1975f21 100644
--- a/SRC/dptsv.f
+++ b/SRC/dptsv.f
@@ -84,7 +84,7 @@
          RETURN
       END IF
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
       CALL DPTTRF( N, D, E, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dptsvx.f b/SRC/dptsvx.f
index 6717ea51..9b4fd274 100644
--- a/SRC/dptsvx.f
+++ b/SRC/dptsvx.f
@@ -188,7 +188,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the L*D*L' (or U'*D*U) factorization of A.
+*        Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
          CALL DCOPY( N, D, 1, DF, 1 )
          IF( N.GT.1 )
diff --git a/SRC/dpttrf.f b/SRC/dpttrf.f
index dae49d23..adffa113 100644
--- a/SRC/dpttrf.f
+++ b/SRC/dpttrf.f
@@ -15,9 +15,9 @@
 *  Purpose
 *  =======
 *
-*  DPTTRF computes the L*D*L' factorization of a real symmetric
+*  DPTTRF computes the L*D*L**T factorization of a real symmetric
 *  positive definite tridiagonal matrix A.  The factorization may also
-*  be regarded as having the form A = U'*D*U.
+*  be regarded as having the form A = U**T*D*U.
 *
 *  Arguments
 *  =========
@@ -28,14 +28,14 @@
 *  D       (input/output) DOUBLE PRECISION array, dimension (N)
 *          On entry, the n diagonal elements of the tridiagonal matrix
 *          A.  On exit, the n diagonal elements of the diagonal matrix
-*          D from the L*D*L' factorization of A.
+*          D from the L*D*L**T factorization of A.
 *
 *  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
 *          matrix A.  On exit, the (n-1) subdiagonal elements of the
-*          unit bidiagonal factor L from the L*D*L' factorization of A.
+*          unit bidiagonal factor L from the L*D*L**T factorization of A.
 *          E can also be regarded as the superdiagonal of the unit
-*          bidiagonal factor U from the U'*D*U factorization of A.
+*          bidiagonal factor U from the U**T*D*U factorization of A.
 *
 *  INFO    (output) INTEGER
 *          = 0: successful exit
@@ -77,7 +77,7 @@
       IF( N.EQ.0 )
      $   RETURN
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
       I4 = MOD( N-1, 4 )
       DO 10 I = 1, I4
diff --git a/SRC/dpttrs.f b/SRC/dpttrs.f
index b12a905c..d0ea407e 100644
--- a/SRC/dpttrs.f
+++ b/SRC/dpttrs.f
@@ -17,7 +17,7 @@
 *
 *  DPTTRS solves a tridiagonal system of the form
 *     A * X = B
-*  using the L*D*L' factorization of A computed by DPTTRF.  D is a
+*  using the L*D*L**T factorization of A computed by DPTTRF.  D is a
 *  diagonal matrix specified in the vector D, L is a unit bidiagonal
 *  matrix whose subdiagonal is specified in the vector E, and X and B
 *  are N by NRHS matrices.
@@ -34,13 +34,13 @@
 *
 *  D       (input) DOUBLE PRECISION array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          L*D*L' factorization of A.
+*          L*D*L**T factorization of A.
 *
 *  E       (input) DOUBLE PRECISION array, dimension (N-1)
 *          The (n-1) subdiagonal elements of the unit bidiagonal factor
-*          L from the L*D*L' factorization of A.  E can also be regarded
+*          L from the L*D*L**T factorization of A.  E can also be regarded
 *          as the superdiagonal of the unit bidiagonal factor U from the
-*          factorization A = U'*D*U.
+*          factorization A = U**T*D*U.
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
diff --git a/SRC/dptts2.f b/SRC/dptts2.f
index 17abc096..f5e1aa74 100644
--- a/SRC/dptts2.f
+++ b/SRC/dptts2.f
@@ -17,7 +17,7 @@
 *
 *  DPTTS2 solves a tridiagonal system of the form
 *     A * X = B
-*  using the L*D*L' factorization of A computed by DPTTRF.  D is a
+*  using the L*D*L**T factorization of A computed by DPTTRF.  D is a
 *  diagonal matrix specified in the vector D, L is a unit bidiagonal
 *  matrix whose subdiagonal is specified in the vector E, and X and B
 *  are N by NRHS matrices.
@@ -34,13 +34,13 @@
 *
 *  D       (input) DOUBLE PRECISION array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          L*D*L' factorization of A.
+*          L*D*L**T factorization of A.
 *
 *  E       (input) DOUBLE PRECISION array, dimension (N-1)
 *          The (n-1) subdiagonal elements of the unit bidiagonal factor
-*          L from the L*D*L' factorization of A.  E can also be regarded
+*          L from the L*D*L**T factorization of A.  E can also be regarded
 *          as the superdiagonal of the unit bidiagonal factor U from the
-*          factorization A = U'*D*U.
+*          factorization A = U**T*D*U.
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
@@ -68,7 +68,7 @@
          RETURN
       END IF
 *
-*     Solve A * X = B using the factorization A = L*D*L',
+*     Solve A * X = B using the factorization A = L*D*L**T,
 *     overwriting each right hand side vector with its solution.
 *
       DO 30 J = 1, NRHS
@@ -79,7 +79,7 @@
             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
    10    CONTINUE
 *
-*           Solve D * L' * x = b.
+*           Solve D * L**T * x = b.
 *
          B( N, J ) = B( N, J ) / D( N )
          DO 20 I = N - 1, 1, -1
diff --git a/SRC/dspcon.f b/SRC/dspcon.f
index c3467fea..f145711f 100644
--- a/SRC/dspcon.f
+++ b/SRC/dspcon.f
@@ -145,7 +145,7 @@
       CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL DSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/dspgst.f b/SRC/dspgst.f
index d806c5d4..86729f6a 100644
--- a/SRC/dspgst.f
+++ b/SRC/dspgst.f
@@ -102,7 +102,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**T)*A*inv(U)
 *
 *           J1 and JJ are the indices of A(1,j) and A(j,j)
 *
@@ -124,7 +124,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**T)
 *
 *           KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
 *
@@ -154,7 +154,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**T
 *
 *           K1 and KK are the indices of A(1,k) and A(k,k)
 *
@@ -179,7 +179,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**T *A*L
 *
 *           JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
 *
diff --git a/SRC/dspgv.f b/SRC/dspgv.f
index 918d7efa..93692752 100644
--- a/SRC/dspgv.f
+++ b/SRC/dspgv.f
@@ -159,7 +159,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -175,7 +175,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dspgvd.f b/SRC/dspgvd.f
index 63ffad0c..323645a3 100644
--- a/SRC/dspgvd.f
+++ b/SRC/dspgvd.f
@@ -191,7 +191,6 @@
          END IF
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
-*
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -11
          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
@@ -237,7 +236,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -253,7 +252,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T *y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dspgvx.f b/SRC/dspgvx.f
index 0747ff8a..11c88f5a 100644
--- a/SRC/dspgvx.f
+++ b/SRC/dspgvx.f
@@ -255,7 +255,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -271,7 +271,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dspsv.f b/SRC/dspsv.f
index 3c04c48e..7af58c4b 100644
--- a/SRC/dspsv.f
+++ b/SRC/dspsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL DSPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dspsvx.f b/SRC/dspsvx.f
index aa038943..6f1da4bf 100644
--- a/SRC/dspsvx.f
+++ b/SRC/dspsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL DCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL DSPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/dsptrd.f b/SRC/dsptrd.f
index f91adbdc..331dd2af 100644
--- a/SRC/dsptrd.f
+++ b/SRC/dsptrd.f
@@ -73,7 +73,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
@@ -86,7 +86,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
@@ -141,7 +141,7 @@
          I1 = N*( N-1 ) / 2 + 1
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)
 *
             CALL DLARFG( I, AP( I1+I-1 ), AP( I1 ), 1, TAUI )
@@ -158,13 +158,13 @@
                CALL DSPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
      $                     1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, AP( I1 ), 1 )
                CALL DAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL DSPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
 *
@@ -184,7 +184,7 @@
          DO 20 I = 1, N - 1
             I1I1 = II + N - I + 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)
 *
             CALL DLARFG( N-I, AP( II+1 ), AP( II+2 ), 1, TAUI )
@@ -201,14 +201,14 @@
                CALL DSPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
      $                     ZERO, TAU( I ), 1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, AP( II+1 ),
      $                 1 )
                CALL DAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**T
 *
                CALL DSPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
      $                     AP( I1I1 ) )
diff --git a/SRC/dsptrf.f b/SRC/dsptrf.f
index 58538915..889596b1 100644
--- a/SRC/dsptrf.f
+++ b/SRC/dsptrf.f
@@ -71,7 +71,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -88,7 +88,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -153,7 +153,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -274,7 +274,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = ONE / AP( KC+K-1 )
                CALL DSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -293,8 +293,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -340,7 +340,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -468,7 +468,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = ONE / AP( KC )
                   CALL DSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -491,8 +491,11 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
+*
+*                 where L(k) and L(k+1) are the k-th and (k+1)-th
+*                 columns of L
 *
                   D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
                   D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
diff --git a/SRC/dsptri.f b/SRC/dsptri.f
index bc69a179..48b0eb0a 100644
--- a/SRC/dsptri.f
+++ b/SRC/dsptri.f
@@ -127,7 +127,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -228,7 +228,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/dsptrs.f b/SRC/dsptrs.f
index 1fd67b5e..26e6b955 100644
--- a/SRC/dsptrs.f
+++ b/SRC/dsptrs.f
@@ -103,7 +103,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -177,7 +177,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -212,7 +212,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -234,7 +234,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -311,7 +311,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -330,7 +330,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -347,7 +347,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/dsycon.f b/SRC/dsycon.f
index 6326a1c8..209ea1c8 100644
--- a/SRC/dsycon.f
+++ b/SRC/dsycon.f
@@ -148,7 +148,7 @@
       CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/dsygs2.f b/SRC/dsygs2.f
index 7d0f87ca..100c99d3 100644
--- a/SRC/dsygs2.f
+++ b/SRC/dsygs2.f
@@ -20,19 +20,19 @@
 *  to standard form.
 *
 *  If ITYPE = 1, the problem is A*x = lambda*B*x,
-*  and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
+*  and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
 *
 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-*  B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
+*  B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
 *
-*  B must have been previously factorized as U'*U or L*L' by DPOTRF.
+*  B must have been previously factorized as U**T *U or L*L**T by DPOTRF.
 *
 *  Arguments
 *  =========
 *
 *  ITYPE   (input) INTEGER
-*          = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
-*          = 2 or 3: compute U*A*U' or L'*A*L.
+*          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
+*          = 2 or 3: compute U*A*U**T or L**T *A*L.
 *
 *  UPLO    (input) CHARACTER*1
 *          Specifies whether the upper or lower triangular part of the
@@ -115,7 +115,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**T)*A*inv(U)
 *
             DO 10 K = 1, N
 *
@@ -140,7 +140,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**T)
 *
             DO 20 K = 1, N
 *
@@ -165,7 +165,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**T
 *
             DO 30 K = 1, N
 *
@@ -185,7 +185,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**T *A*L
 *
             DO 40 K = 1, N
 *
diff --git a/SRC/dsygst.f b/SRC/dsygst.f
index c1b2a955..97ad94c2 100644
--- a/SRC/dsygst.f
+++ b/SRC/dsygst.f
@@ -133,7 +133,7 @@
          IF( ITYPE.EQ.1 ) THEN
             IF( UPPER ) THEN
 *
-*              Compute inv(U')*A*inv(U)
+*              Compute inv(U**T)*A*inv(U)
 *
                DO 10 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -163,7 +163,7 @@
    10          CONTINUE
             ELSE
 *
-*              Compute inv(L)*A*inv(L')
+*              Compute inv(L)*A*inv(L**T)
 *
                DO 20 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -195,7 +195,7 @@
          ELSE
             IF( UPPER ) THEN
 *
-*              Compute U*A*U'
+*              Compute U*A*U**T
 *
                DO 30 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -219,7 +219,7 @@
    30          CONTINUE
             ELSE
 *
-*              Compute L'*A*L
+*              Compute L**T*A*L
 *
                DO 40 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
diff --git a/SRC/dsygv.f b/SRC/dsygv.f
index 43607d36..9fc2c250 100644
--- a/SRC/dsygv.f
+++ b/SRC/dsygv.f
@@ -195,7 +195,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -209,7 +209,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dsygvd.f b/SRC/dsygvd.f
index f123fa84..857abfd8 100644
--- a/SRC/dsygvd.f
+++ b/SRC/dsygvd.f
@@ -246,7 +246,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -260,7 +260,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dsygvx.f b/SRC/dsygvx.f
index b0108d96..e70009df 100644
--- a/SRC/dsygvx.f
+++ b/SRC/dsygvx.f
@@ -296,7 +296,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -310,7 +310,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/dsysv.f b/SRC/dsysv.f
index 65ba671c..5979f38b 100644
--- a/SRC/dsysv.f
+++ b/SRC/dsysv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/dsysvx.f b/SRC/dsysvx.f
index 89ae68fe..3149606d 100644
--- a/SRC/dsysvx.f
+++ b/SRC/dsysvx.f
@@ -254,7 +254,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL DLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL DSYTRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/dsytd2.f b/SRC/dsytd2.f
index f3e6f0a9..da799b95 100644
--- a/SRC/dsytd2.f
+++ b/SRC/dsytd2.f
@@ -17,7 +17,7 @@
 *  =======
 *
 *  DSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
-*  form T by an orthogonal similarity transformation: Q' * A * Q = T.
+*  form T by an orthogonal similarity transformation: Q**T * A * Q = T.
 *
 *  Arguments
 *  =========
@@ -79,7 +79,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -164,7 +164,7 @@
 *
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)
 *
             CALL DLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI )
@@ -181,13 +181,13 @@
                CALL DSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
      $                     TAU, 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, A( 1, I+1 ), 1 )
                CALL DAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL DSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
      $                     LDA )
@@ -204,7 +204,7 @@
 *
          DO 20 I = 1, N - 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)
 *
             CALL DLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,
@@ -222,14 +222,14 @@
                CALL DSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
      $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, A( I+1, I ),
      $                 1 )
                CALL DAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**T
 *
                CALL DSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )
diff --git a/SRC/dsytf2.f b/SRC/dsytf2.f
index 261651fe..689ef119 100644
--- a/SRC/dsytf2.f
+++ b/SRC/dsytf2.f
@@ -20,10 +20,10 @@
 *  DSYTF2 computes the factorization of a real symmetric matrix A using
 *  the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**T  or  A = L*D*L**T
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the transpose of U, and D is symmetric and
+*  triangular matrices, U**T is the transpose of U, and D is symmetric and
 *  block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -90,7 +90,7 @@
 *  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -107,7 +107,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -173,7 +173,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -279,7 +279,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = ONE / A( K, K )
                CALL DSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -298,8 +298,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -341,7 +341,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -450,7 +450,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   D11 = ONE / A( K, K )
                   CALL DSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
@@ -468,7 +468,7 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( (A(k) A(k+1))*D(k)**(-1) ) * (A(k) A(k+1))'
+*                 A := A - ( (A(k) A(k+1))*D(k)**(-1) ) * (A(k) A(k+1))**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/dsytrd.f b/SRC/dsytrd.f
index befbee31..1bc8fec6 100644
--- a/SRC/dsytrd.f
+++ b/SRC/dsytrd.f
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -105,7 +105,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -235,7 +235,7 @@
      $                   LDWORK )
 *
 *           Update the unreduced submatrix A(1:i-1,1:i-1), using an
-*           update of the form:  A := A - V*W' - W*V'
+*           update of the form:  A := A - V*W' - W*V**T
 *
             CALL DSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
      $                   LDA, WORK, LDWORK, ONE, A, LDA )
@@ -266,7 +266,7 @@
      $                   TAU( I ), WORK, LDWORK )
 *
 *           Update the unreduced submatrix A(i+ib:n,i+ib:n), using
-*           an update of the form:  A := A - V*W' - W*V'
+*           an update of the form:  A := A - V*W' - W*V**T
 *
             CALL DSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
      $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
diff --git a/SRC/dsytrf.f b/SRC/dsytrf.f
index e0a1b191..377aa21d 100644
--- a/SRC/dsytrf.f
+++ b/SRC/dsytrf.f
@@ -87,7 +87,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -187,7 +187,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by DLASYF;
@@ -228,7 +228,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by DLASYF;
diff --git a/SRC/dsytri.f b/SRC/dsytri.f
index 4cbc40ec..3e7d88e5 100644
--- a/SRC/dsytri.f
+++ b/SRC/dsytri.f
@@ -127,7 +127,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -216,7 +216,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/dsytri2x.f b/SRC/dsytri2x.f
index d0481f56..52d99532 100644
--- a/SRC/dsytri2x.f
+++ b/SRC/dsytri2x.f
@@ -153,7 +153,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
         CALL DTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -181,9 +181,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -309,7 +309,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -331,7 +331,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
          CALL DTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -359,9 +359,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -495,7 +495,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/dsytrs.f b/SRC/dsytrs.f
index 65cc7296..7a4a0f77 100644
--- a/SRC/dsytrs.f
+++ b/SRC/dsytrs.f
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -178,7 +178,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -211,7 +211,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -232,7 +232,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -306,7 +306,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -323,7 +323,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -340,7 +340,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/dsytrs2.f b/SRC/dsytrs2.f
index 3e2e6748..9e256d85 100644
--- a/SRC/dsytrs2.f
+++ b/SRC/dsytrs2.f
@@ -116,9 +116,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
-*       P' * B  
+*       P**T * B  
         K=N
         DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN
@@ -138,11 +138,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -166,11 +166,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**T \ B) -> B   [ U**T \ (D \ (U \P**T * B) ) ]
 *
          CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**T \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -193,9 +193,9 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
-*       P' * B  
+*       P**T * B  
         K=1
         DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN
@@ -215,11 +215,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -241,11 +241,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**T \ B) -> B   [ L**T \ (D \ (L \P**T * B) ) ]
 * 
         CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**T \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/dtbrfs.f b/SRC/dtbrfs.f
index c15bf9ce..2c56acd0 100644
--- a/SRC/dtbrfs.f
+++ b/SRC/dtbrfs.f
@@ -348,7 +348,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL DTBSV( UPLO, TRANST, DIAG, N, KD, AB, LDAB,
      $                     WORK( N+1 ), 1 )
diff --git a/SRC/dtgex2.f b/SRC/dtgex2.f
index 9334ba82..9362fe21 100644
--- a/SRC/dtgex2.f
+++ b/SRC/dtgex2.f
@@ -29,8 +29,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
+*         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
 *
 *
 *  Arguments
@@ -259,7 +259,7 @@
          IF( WANDS ) THEN
 *
 *           Strong stability test:
-*             F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B)))
+*             F-norm((A-QL**T*S*QR, B-QL**T*T*QR)) <= O(EPS*F-norm((A,B)))
 *
             CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
      $                   M )
@@ -334,8 +334,8 @@
 *
 *        Compute orthogonal matrix QL:
 *
-*                    QL' * LI = [ TL ]
-*                               [ 0  ]
+*                    QL**T * LI = [ TL ]
+*                                 [ 0  ]
 *        where
 *                    LI =  [      -L              ]
 *                          [ SCALE * identity(N2) ]
@@ -353,7 +353,7 @@
 *
 *        Compute orthogonal matrix RQ:
 *
-*                    IR * RQ' =   [ 0  TR],
+*                    IR * RQ**T =   [ 0  TR],
 *
 *         where IR = [ SCALE * identity(N1), R ]
 *
@@ -448,7 +448,7 @@
          IF( WANDS ) THEN
 *
 *           Strong stability test:
-*              F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B)))
+*              F-norm((A-QL*S*QR**T, B-QL*T*QR**T)) <= O(EPS*F-norm((A,B)))
 *
             CALL DLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
      $                   M )
diff --git a/SRC/dtgexc.f b/SRC/dtgexc.f
index 4262778f..56158d45 100644
--- a/SRC/dtgexc.f
+++ b/SRC/dtgexc.f
@@ -33,8 +33,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
+*         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
 *
 *
 *  Arguments
diff --git a/SRC/dtgsen.f b/SRC/dtgsen.f
index 5c269fd0..583d087f 100644
--- a/SRC/dtgsen.f
+++ b/SRC/dtgsen.f
@@ -28,7 +28,7 @@
 *
 *  DTGSEN reorders the generalized real Schur decomposition of a real
 *  matrix pair (A, B) (in terms of an orthonormal equivalence trans-
-*  formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues
+*  formation Q**T * (A, B) * Z), so that a selected cluster of eigenvalues
 *  appears in the leading diagonal blocks of the upper quasi-triangular
 *  matrix A and the upper triangular B. The leading columns of Q and
 *  Z form orthonormal bases of the corresponding left and right eigen-
@@ -208,7 +208,7 @@
 *  In other words, the selected eigenvalues are the eigenvalues of
 *  (A11, B11) in:
 *
-*                U'*(A, B)*W = (A11 A12) (B11 B12) n1
+*              U**T*(A, B)*W = (A11 A12) (B11 B12) n1
 *                              ( 0  A22),( 0  B22) n2
 *                                n1  n2    n1  n2
 *
@@ -217,10 +217,10 @@
 *  (deflating subspaces) of (A, B).
 *
 *  If (A, B) has been obtained from the generalized real Schur
-*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the
+*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z**T, then the
 *  reordered generalized real Schur form of (C, D) is given by
 *
-*           (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',
+*           (C, D) = (Q*U)*(U**T*(A, B)*W)*(Z*W)**T,
 *
 *  and the first n1 columns of Q*U and Z*W span the corresponding
 *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).
@@ -242,10 +242,10 @@
 *  where sigma-min(Zu) is the smallest singular value of the
 *  (2*n1*n2)-by-(2*n1*n2) matrix
 *
-*       Zu = [ kron(In2, A11)  -kron(A22', In1) ]
-*            [ kron(In2, B11)  -kron(B22', In1) ].
+*       Zu = [ kron(In2, A11)  -kron(A22**T, In1) ]
+*            [ kron(In2, B11)  -kron(B22**T, In1) ].
 *
-*  Here, Inx is the identity matrix of size nx and A22' is the
+*  Here, Inx is the identity matrix of size nx and A22**T is the
 *  transpose of A22. kron(X, Y) is the Kronecker product between
 *  the matrices X and Y.
 *
diff --git a/SRC/dtgsja.f b/SRC/dtgsja.f
index cd011e81..1cb3b244 100644
--- a/SRC/dtgsja.f
+++ b/SRC/dtgsja.f
@@ -48,10 +48,10 @@
 *
 *  On exit,
 *
-*              U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R ),
+*         U**T *A*Q = D1*( 0 R ),    V**T *B*Q = D2*( 0 R ),
 *
-*  where U, V and Q are orthogonal matrices, Z' denotes the transpose
-*  of Z, R is a nonsingular upper triangular matrix, and D1 and D2 are
+*  where U, V and Q are orthogonal matrices.
+*  R is a nonsingular upper triangular matrix, and D1 and D2 are
 *  ``diagonal'' matrices, which are of the following structures:
 *
 *  If M-K-L >= 0,
@@ -247,7 +247,7 @@
 *  min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
 *  matrix B13 to the form:
 *
-*           U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
+*           U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1,
 *
 *  where U1, V1 and Q1 are orthogonal matrix, and Z' is the transpose
 *  of Z.  C1 and S1 are diagonal matrices satisfying
@@ -367,13 +367,13 @@
                CALL DLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
      $                      CSV, SNV, CSQ, SNQ )
 *
-*              Update (K+I)-th and (K+J)-th rows of matrix A: U'*A
+*              Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A
 *
                IF( K+J.LE.M )
      $            CALL DROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
      $                       LDA, CSU, SNU )
 *
-*              Update I-th and J-th rows of matrix B: V'*B
+*              Update I-th and J-th rows of matrix B: V**T *B
 *
                CALL DROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
      $                    CSV, SNV )
diff --git a/SRC/dtgsna.f b/SRC/dtgsna.f
index 2b2c4fea..4f3d1dc7 100644
--- a/SRC/dtgsna.f
+++ b/SRC/dtgsna.f
@@ -24,7 +24,7 @@
 *  DTGSNA estimates reciprocal condition numbers for specified
 *  eigenvalues and/or eigenvectors of a matrix pair (A, B) in
 *  generalized real Schur canonical form (or of any matrix pair
-*  (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where
+*  (Q*A*Z**T, Q*B*Z**T) with orthogonal matrices Q and Z, where
 *  Z' denotes the transpose of Z.
 *
 *  (A, B) must be in generalized real Schur form (as returned by DGGES),
@@ -150,12 +150,12 @@
 *  The reciprocal of the condition number of a generalized eigenvalue
 *  w = (a, b) is defined as
 *
-*       S(w) = (|u'Av|**2 + |u'Bv|**2)**(1/2) / (norm(u)*norm(v))
+*       S(w) = (|u**TAv|**2 + |u**TBv|**2)**(1/2) / (norm(u)*norm(v))
 *
 *  where u and v are the left and right eigenvectors of (A, B)
 *  corresponding to w; |z| denotes the absolute value of the complex
 *  number, and norm(u) denotes the 2-norm of the vector u.
-*  The pair (a, b) corresponds to an eigenvalue w = a/b (= u'Av/u'Bv)
+*  The pair (a, b) corresponds to an eigenvalue w = a/b (= u**TAv/u**TBv)
 *  of the matrix pair (A, B). If both a and b equal zero, then (A B) is
 *  singular and S(I) = -1 is returned.
 *
@@ -175,7 +175,7 @@
 *
 *     Suppose U and V are orthogonal transformations such that
 *
-*                U'*(A, B)*V  = (S, T) = ( a   *  ) ( b  *  )  1
+*              U**T*(A, B)*V  = (S, T) = ( a   *  ) ( b  *  )  1
 *                                        ( 0  S22 ),( 0 T22 )  n-1
 *                                          1  n-1     1 n-1
 *
@@ -201,7 +201,7 @@
 *
 *     Suppose U and V are orthogonal transformations such that
 *
-*                U'*(A, B)*V = (S, T) = ( S11  *   ) ( T11  *  )  2
+*              U**T*(A, B)*V = (S, T) = ( S11  *   ) ( T11  *  )  2
 *                                       ( 0    S22 ),( 0    T22) n-2
 *                                         2    n-2     2    n-2
 *
@@ -209,7 +209,7 @@
 *     pair (w, conjg(w)). There exist unitary matrices U1 and V1 such
 *     that
 *
-*         U1'*S11*V1 = ( s11 s12 )   and U1'*T11*V1 = ( t11 t12 )
+*       U1**T*S11*V1 = ( s11 s12 ) and U1**T*T11*V1 = ( t11 t12 )
 *                      (  0  s22 )                    (  0  t22 )
 *
 *     where the generalized eigenvalues w = s11/t11 and
@@ -226,8 +226,8 @@
 *                    [ t11  -t22 ],
 *
 *     This is done by computing (using real arithmetic) the
-*     roots of the characteristical polynomial det(Z1' * Z1 - lambda I),
-*     where Z1' denotes the conjugate transpose of Z1 and det(X) denotes
+*     roots of the characteristical polynomial det(Z1**T * Z1 - lambda I),
+*     where Z1**T denotes the transpose of Z1 and det(X) denotes
 *     the determinant of X.
 *
 *     and d2 is an upper bound on Difl((S11, T11), (S22, T22)), i.e. an
diff --git a/SRC/dtgsy2.f b/SRC/dtgsy2.f
index c86a2351..72dcf698 100644
--- a/SRC/dtgsy2.f
+++ b/SRC/dtgsy2.f
@@ -628,7 +628,7 @@
       ELSE
 *
 *        Solve (I, J) - subsystem
-*             A(I, I)' * R(I, J) + D(I, I)' * L(J, J)  =  C(I, J)
+*             A(I, I)**T * R(I, J) + D(I, I)**T * L(J, J)  =  C(I, J)
 *             R(I, I)  * B(J, J) + L(I, J)  * E(J, J)  = -F(I, J)
 *        for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1
 *
diff --git a/SRC/dtgsyl.f b/SRC/dtgsyl.f
index 3712c07f..1b82a5c9 100644
--- a/SRC/dtgsyl.f
+++ b/SRC/dtgsyl.f
@@ -46,11 +46,11 @@
 *  Here Ik is the identity matrix of size k and X' is the transpose of
 *  X. kron(X, Y) is the Kronecker product between the matrices X and Y.
 *
-*  If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b,
+*  If TRANS = 'T', DTGSYL solves the transposed system Z**T*y = scale*b,
 *  which is equivalent to solve for R and L in
 *
-*              A' * R  + D' * L   = scale *  C           (3)
-*              R  * B' + L  * E'  = scale * (-F)
+*              A**T * R + D**T * L = scale * C           (3)
+*              R * B**T + L * E**T = scale * -F
 *
 *  This case (TRANS = 'T') is used to compute an one-norm-based estimate
 *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
@@ -485,8 +485,8 @@
       ELSE
 *
 *        Solve transposed (I, J)-subsystem
-*             A(I, I)' * R(I, J)  + D(I, I)' * L(I, J)  =  C(I, J)
-*             R(I, J)  * B(J, J)' + L(I, J)  * E(J, J)' = -F(I, J)
+*             A(I, I)**T * R(I, J)  + D(I, I)**T * L(I, J)  =  C(I, J)
+*             R(I, J)  * B(J, J)**T + L(I, J)  * E(J, J)**T = -F(I, J)
 *        for I = 1,2,..., P; J = Q, Q-1,..., 1
 *
          SCALE = ONE
diff --git a/SRC/dtprfs.f b/SRC/dtprfs.f
index c5d1ee82..f0ac8d38 100644
--- a/SRC/dtprfs.f
+++ b/SRC/dtprfs.f
@@ -344,7 +344,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL DTPSV( UPLO, TRANST, DIAG, N, AP, WORK( N+1 ), 1 )
                DO 220 I = 1, N
diff --git a/SRC/dtrevc.f b/SRC/dtrevc.f
index bbb2d456..a37e2264 100644
--- a/SRC/dtrevc.f
+++ b/SRC/dtrevc.f
@@ -27,9 +27,9 @@
 *  The right eigenvector x and the left eigenvector y of T corresponding
 *  to an eigenvalue w are defined by:
 *  
-*     T*x = w*x,     (y**H)*T = w*(y**H)
+*     T*x = w*x,     (y**T)*T = w*(y**T)
 *  
-*  where y**H denotes the conjugate transpose of y.
+*  where y**T denotes the transpose of y.
 *  The eigenvalues are not input to this routine, but are read directly
 *  from the diagonal blocks of T.
 *  
@@ -651,7 +651,7 @@
   160          CONTINUE
 *
 *              Solve the quasi-triangular system:
-*                 (T(KI+1:N,KI+1:N) - WR)'*X = SCALE*WORK
+*                 (T(KI+1:N,KI+1:N) - WR)**T*X = SCALE*WORK
 *
                VMAX = ONE
                VCRIT = BIGNUM
@@ -688,7 +688,7 @@
      $                             DDOT( J-KI-1, T( KI+1, J ), 1,
      $                             WORK( KI+1+N ), 1 )
 *
-*                    Solve (T(J,J)-WR)'*X = WORK
+*                    Solve (T(J,J)-WR)**T*X = WORK
 *
                      CALL DLALN2( .FALSE., 1, 1, SMIN, ONE, T( J, J ),
      $                            LDT, ONE, ONE, WORK( J+N ), N, WR,
@@ -778,7 +778,7 @@
 *              Complex left eigenvector.
 *
 *               Initial solve:
-*                 ((T(KI,KI)    T(KI,KI+1) )' - (WR - I* WI))*X = 0.
+*                 ((T(KI,KI)    T(KI,KI+1) )**T - (WR - I* WI))*X = 0.
 *                 ((T(KI+1,KI) T(KI+1,KI+1))                )
 *
                IF( ABS( T( KI, KI+1 ) ).GE.ABS( T( KI+1, KI ) ) ) THEN
diff --git a/SRC/dtrrfs.f b/SRC/dtrrfs.f
index 4ecf6fa1..49fedcc8 100644
--- a/SRC/dtrrfs.f
+++ b/SRC/dtrrfs.f
@@ -338,7 +338,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL DTRSV( UPLO, TRANST, DIAG, N, A, LDA, WORK( N+1 ),
      $                     1 )
diff --git a/SRC/dtrsen.f b/SRC/dtrsen.f
index 28e62c62..ba5528ce 100644
--- a/SRC/dtrsen.f
+++ b/SRC/dtrsen.f
@@ -156,7 +156,7 @@
 *  In other words, the selected eigenvalues are the eigenvalues of T11
 *  in:
 *
-*                Z'*T*Z = ( T11 T12 ) n1
+*          Z**T * T * Z = ( T11 T12 ) n1
 *                         (  0  T22 ) n2
 *                            n1  n2
 *
@@ -164,8 +164,8 @@
 *  of Z span the specified invariant subspace of T.
 *
 *  If T has been obtained from the real Schur factorization of a matrix
-*  A = Q*T*Q', then the reordered real Schur factorization of A is given
-*  by A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span
+*  A = Q*T*Q**T, then the reordered real Schur factorization of A is given
+*  by A = (Q*Z)*(Z**T*T*Z)*(Q*Z)**T, and the first n1 columns of Q*Z span
 *  the corresponding invariant subspace of A.
 *
 *  The reciprocal condition number of the average of the eigenvalues of
@@ -422,7 +422,7 @@
      $                      IERR )
             ELSE
 *
-*              Solve  T11'*R - R*T22' = scale*X.
+*              Solve T11**T*R - R*T22**T = scale*X.
 *
                CALL DTRSYL( 'T', 'T', -1, N1, N2, T, LDT,
      $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
diff --git a/SRC/dtrsna.f b/SRC/dtrsna.f
index 33e1d995..6595d877 100644
--- a/SRC/dtrsna.f
+++ b/SRC/dtrsna.f
@@ -140,10 +140,10 @@
 *  The reciprocal of the condition number of an eigenvalue lambda is
 *  defined as
 *
-*          S(lambda) = |v'*u| / (norm(u)*norm(v))
+*          S(lambda) = |v**T*u| / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of T corresponding
-*  to lambda; v' denotes the conjugate-transpose of v, and norm(u)
+*  to lambda; v**T denotes the transpose of v, and norm(u)
 *  denotes the Euclidean norm. These reciprocal condition numbers always
 *  lie between zero (very badly conditioned) and one (very well
 *  conditioned). If n = 1, S(lambda) is defined to be 1.
@@ -403,12 +403,12 @@
 *
 *                 Form
 *
-*                 C' = WORK(2:N,2:N) + i*[rwork(1) ..... rwork(n-1) ]
-*                                        [   mu                     ]
-*                                        [         ..               ]
-*                                        [             ..           ]
-*                                        [                  mu      ]
-*                 where C' is conjugate transpose of complex matrix C,
+*                 C**T = WORK(2:N,2:N) + i*[rwork(1) ..... rwork(n-1) ]
+*                                          [   mu                     ]
+*                                          [         ..               ]
+*                                          [             ..           ]
+*                                          [                  mu      ]
+*                 where C**T is transpose of matrix C,
 *                 and RWORK is stored starting in the N+1-st column of
 *                 WORK.
 *
@@ -426,7 +426,7 @@
                   NN = 2*( N-1 )
                END IF
 *
-*              Estimate norm(inv(C'))
+*              Estimate norm(inv(C**T))
 *
                EST = ZERO
                KASE = 0
@@ -437,7 +437,7 @@
                   IF( KASE.EQ.1 ) THEN
                      IF( N2.EQ.1 ) THEN
 *
-*                       Real eigenvalue: solve C'*x = scale*c.
+*                       Real eigenvalue: solve C**T*x = scale*c.
 *
                         CALL DLAQTR( .TRUE., .TRUE., N-1, WORK( 2, 2 ),
      $                               LDWORK, DUMMY, DUMM, SCALE,
@@ -446,7 +446,7 @@
                      ELSE
 *
 *                       Complex eigenvalue: solve
-*                       C'*(p+iq) = scale*(c+id) in real arithmetic.
+*                       C**T*(p+iq) = scale*(c+id) in real arithmetic.
 *
                         CALL DLAQTR( .TRUE., .FALSE., N-1, WORK( 2, 2 ),
      $                               LDWORK, WORK( 1, N+1 ), MU, SCALE,
diff --git a/SRC/dtrsyl.f b/SRC/dtrsyl.f
index ec3e23d7..e63db3c5 100644
--- a/SRC/dtrsyl.f
+++ b/SRC/dtrsyl.f
@@ -355,17 +355,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
 *
-*        Solve    A' *X + ISGN*X*B = scale*C.
+*        Solve    A**T *X + ISGN*X*B = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-left corner column by column by
 *
-*          A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
+*          A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
 *
 *        Where
-*                   K-1                        L-1
-*          R(K,L) = SUM [A(I,K)'*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
-*                   I=1                        J=1
+*                   K-1                          L-1
+*          R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
+*                   I=1                          J=1
 *
 *        Start column loop (index = L)
 *        L1 (L2): column index of the first (last) row of X(K,L)
@@ -530,17 +530,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A'*X + ISGN*X*B' = scale*C.
+*        Solve    A**T*X + ISGN*X*B**T = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        top-right corner column by column by
 *
-*           A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L)
+*           A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
 *
 *        Where
-*                     K-1                          N
-*            R(K,L) = SUM [A(I,K)'*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)'].
-*                     I=1                        J=L+1
+*                     K-1                            N
+*            R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T].
+*                     I=1                          J=L+1
 *
 *        Start column loop (index = L)
 *        L1 (L2): column index of the first (last) row of X(K,L)
@@ -714,16 +714,16 @@
 *
       ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A*X + ISGN*X*B' = scale*C.
+*        Solve    A*X + ISGN*X*B**T = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        bottom-right corner column by column by
 *
-*            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L)
+*            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
 *
 *        Where
 *                      M                          N
-*            R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)'].
+*            R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T].
 *                    I=K+1                      J=L+1
 *
 *        Start column loop (index = L)
diff --git a/SRC/dtzrqf.f b/SRC/dtzrqf.f
index 5652be50..cbec29e8 100644
--- a/SRC/dtzrqf.f
+++ b/SRC/dtzrqf.f
@@ -66,9 +66,9 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
-*                                                 (   0    )
-*                                                 ( z( k ) )
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
+*                                                   (   0    )
+*                                                   ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an ( n - m ) element vector.
 *  tau and z( k ) are chosen to annihilate the elements of the kth row
@@ -149,7 +149,7 @@
      $                     LDA, A( K, M1 ), LDA, ONE, TAU, 1 )
 *
 *              Now form  a( k ) := a( k ) - tau*w
-*              and       B      := B      - tau*w*z( k )'.
+*              and       B      := B      - tau*w*z( k )**T.
 *
                CALL DAXPY( K-1, -TAU( K ), TAU, 1, A( 1, K ), 1 )
                CALL DGER( K-1, N-M, -TAU( K ), TAU, 1, A( K, M1 ), LDA,
diff --git a/SRC/dtzrzf.f b/SRC/dtzrzf.f
index 1a4c307f..bf7135b6 100644
--- a/SRC/dtzrzf.f
+++ b/SRC/dtzrzf.f
@@ -81,7 +81,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/sgbbrd.f b/SRC/sgbbrd.f
index ccf61e0c..b2193861 100644
--- a/SRC/sgbbrd.f
+++ b/SRC/sgbbrd.f
@@ -19,20 +19,20 @@
 *  =======
 *
 *  SGBBRD reduces a real general m-by-n band matrix A to upper
-*  bidiagonal form B by an orthogonal transformation: Q' * A * P = B.
+*  bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
 *
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
+*  The routine computes B, and optionally forms Q or P**T, or computes
+*  Q**T*C for a given matrix C.
 *
 *  Arguments
 *  =========
 *
 *  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
+*          Specifies whether or not the matrices Q and P**T are to be
 *          formed.
-*          = 'N': do not form Q or P';
+*          = 'N': do not form Q or P**T;
 *          = 'Q': form Q only;
-*          = 'P': form P' only;
+*          = 'P': form P**T only;
 *          = 'B': form both.
 *
 *  M       (input) INTEGER
@@ -85,7 +85,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,NCC)
 *          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
+*          On exit, C is overwritten by Q**T*C.
 *          C is not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
@@ -157,7 +157,7 @@
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**T to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL SLASET( 'Full', M, M, ZERO, ONE, Q, LDQ )
@@ -334,7 +334,7 @@
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**T
 *
                   DO 60 J = J1, J2, KB1
                      CALL SROT( N, PT( J+KUN-1, 1 ), LDPT,
diff --git a/SRC/sgbcon.f b/SRC/sgbcon.f
index b4b3c689..473c4ebb 100644
--- a/SRC/sgbcon.f
+++ b/SRC/sgbcon.f
@@ -179,13 +179,13 @@
      $                   INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL SLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KL+KU, AB, LDAB, WORK, SCALE, WORK( 2*N+1 ),
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             IF( LNOTI ) THEN
                DO 30 J = N - 1, 1, -1
diff --git a/SRC/sgebd2.f b/SRC/sgebd2.f
index 86875f0c..4a782f72 100644
--- a/SRC/sgebd2.f
+++ b/SRC/sgebd2.f
@@ -87,7 +87,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
diff --git a/SRC/sgebrd.f b/SRC/sgebrd.f
index 47eb1e1d..9a49eac5 100644
--- a/SRC/sgebrd.f
+++ b/SRC/sgebrd.f
@@ -99,7 +99,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
@@ -112,7 +112,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
@@ -232,7 +232,7 @@
      $                WORK( LDWRKX*NB+1 ), LDWRKY )
 *
 *        Update the trailing submatrix A(i+nb:m,i+nb:n), using an update
-*        of the form  A := A - V*Y' - X*U'
+*        of the form  A := A - V*Y**T - X*U**T
 *
          CALL SGEMM( 'No transpose', 'Transpose', M-I-NB+1, N-I-NB+1,
      $               NB, -ONE, A( I+NB, I ), LDA,
diff --git a/SRC/sgecon.f b/SRC/sgecon.f
index a2a11126..56c30232 100644
--- a/SRC/sgecon.f
+++ b/SRC/sgecon.f
@@ -149,12 +149,12 @@
      $                   A, LDA, WORK, SU, WORK( 3*N+1 ), INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SU, WORK( 3*N+1 ), INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL SLATRS( 'Lower', 'Transpose', 'Unit', NORMIN, N, A,
      $                   LDA, WORK, SL, WORK( 2*N+1 ), INFO )
diff --git a/SRC/sgeev.f b/SRC/sgeev.f
index d74fe71e..87b9861f 100644
--- a/SRC/sgeev.f
+++ b/SRC/sgeev.f
@@ -25,8 +25,8 @@
 *                   A * v(j) = lambda(j) * v(j)
 *  where lambda(j) is its eigenvalue.
 *  The left eigenvector u(j) of A satisfies
-*                u(j)**H * A = lambda(j) * u(j)**H
-*  where u(j)**H denotes the conjugate transpose of u(j).
+*                u(j)**T * A = lambda(j) * u(j)**T
+*  where u(j)**T denotes the transpose of u(j).
 *
 *  The computed eigenvectors are normalized to have Euclidean norm
 *  equal to 1 and largest component real.
diff --git a/SRC/sgeevx.f b/SRC/sgeevx.f
index b3124a79..483930fe 100644
--- a/SRC/sgeevx.f
+++ b/SRC/sgeevx.f
@@ -35,8 +35,8 @@
 *                   A * v(j) = lambda(j) * v(j)
 *  where lambda(j) is its eigenvalue.
 *  The left eigenvector u(j) of A satisfies
-*                u(j)**H * A = lambda(j) * u(j)**H
-*  where u(j)**H denotes the conjugate transpose of u(j).
+*                u(j)**T * A = lambda(j) * u(j)**T
+*  where u(j)**T denotes the transpose of u(j).
 *
 *  The computed eigenvectors are normalized to have Euclidean norm
 *  equal to 1 and largest component real.
diff --git a/SRC/sgehd2.f b/SRC/sgehd2.f
index f8419d27..466fef45 100644
--- a/SRC/sgehd2.f
+++ b/SRC/sgehd2.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  SGEHD2 reduces a real general matrix A to upper Hessenberg form H by
-*  an orthogonal similarity transformation:  Q' * A * Q = H .
+*  an orthogonal similarity transformation:  Q**T * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -63,7 +63,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
diff --git a/SRC/sgehrd.f b/SRC/sgehrd.f
index 1a76c891..3ba78516 100644
--- a/SRC/sgehrd.f
+++ b/SRC/sgehrd.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  SGEHRD reduces a real general matrix A to upper Hessenberg form H by
-*  an orthogonal similarity transformation:  Q' * A * Q = H .
+*  an orthogonal similarity transformation:  Q**T * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -223,14 +223,14 @@
             IB = MIN( NB, IHI-I )
 *
 *           Reduce columns i:i+ib-1 to Hessenberg form, returning the
-*           matrices V and T of the block reflector H = I - V*T*V'
+*           matrices V and T of the block reflector H = I - V*T*V**T
 *           which performs the reduction, and also the matrix Y = A*V*T
 *
             CALL SLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
      $                   WORK, LDWORK )
 *
 *           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
+*           right, computing  A := A - Y * V**T. V(i+ib,ib-1) must be set
 *           to 1
 *
             EI = A( I+IB, I+IB-1 )
diff --git a/SRC/sgelq2.f b/SRC/sgelq2.f
index 45eee7d6..d7f5c105 100644
--- a/SRC/sgelq2.f
+++ b/SRC/sgelq2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
diff --git a/SRC/sgelqf.f b/SRC/sgelqf.f
index 8eac3023..40140ff4 100644
--- a/SRC/sgelqf.f
+++ b/SRC/sgelqf.f
@@ -68,7 +68,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
diff --git a/SRC/sgels.f b/SRC/sgels.f
index 0c34a0e5..d20e4f02 100644
--- a/SRC/sgels.f
+++ b/SRC/sgels.f
@@ -277,7 +277,7 @@
 *
 *           Least-Squares Problem min || A * X - B ||
 *
-*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
             CALL SORMQR( 'Left', 'Transpose', M, NRHS, N, A, LDA,
      $                   WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
@@ -359,7 +359,7 @@
    30          CONTINUE
    40       CONTINUE
 *
-*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS)
+*           B(1:N,1:NRHS) := Q(1:N,:)**T * B(1:M,1:NRHS)
 *
             CALL SORMLQ( 'Left', 'Transpose', N, NRHS, M, A, LDA,
      $                   WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
diff --git a/SRC/sgelsx.f b/SRC/sgelsx.f
index 409ba1a9..b7ea0f1f 100644
--- a/SRC/sgelsx.f
+++ b/SRC/sgelsx.f
@@ -44,8 +44,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**T [ inv(T11)*Q1**T*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  Arguments
@@ -267,7 +267,7 @@
 *
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
       CALL SORM2R( 'Left', 'Transpose', M, NRHS, MN, A, LDA, WORK( 1 ),
      $             B, LDB, WORK( 2*MN+1 ), INFO )
@@ -285,7 +285,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          DO 50 I = 1, RANK
diff --git a/SRC/sgelsy.f b/SRC/sgelsy.f
index 3a7b84c8..9e7bcd1a 100644
--- a/SRC/sgelsy.f
+++ b/SRC/sgelsy.f
@@ -42,8 +42,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**T [ inv(T11)*Q1**T*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  This routine is basically identical to the original xGELSX except
@@ -325,7 +325,7 @@
 *     workspace: 2*MN.
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**T * B(1:M,1:NRHS)
 *
       CALL SORMQR( 'Left', 'Transpose', M, NRHS, MN, A, LDA, WORK( 1 ),
      $             B, LDB, WORK( 2*MN+1 ), LWORK-2*MN, INFO )
@@ -344,7 +344,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**T * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          CALL SORMRZ( 'Left', 'Transpose', N, NRHS, RANK, N-RANK, A,
diff --git a/SRC/sgeql2.f b/SRC/sgeql2.f
index 35db4a29..91e1aa3b 100644
--- a/SRC/sgeql2.f
+++ b/SRC/sgeql2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
diff --git a/SRC/sgeqlf.f b/SRC/sgeqlf.f
index 79914c29..65aa74a7 100644
--- a/SRC/sgeqlf.f
+++ b/SRC/sgeqlf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -186,7 +186,7 @@
                CALL SLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
      $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
+*              Apply H**T to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
 *
                CALL SLARFB( 'Left', 'Transpose', 'Backward',
      $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
diff --git a/SRC/sgeqp3.f b/SRC/sgeqp3.f
index fdd9170e..12bfb585 100644
--- a/SRC/sgeqp3.f
+++ b/SRC/sgeqp3.f
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real/complex scalar, and v is a real/complex vector
 *  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
diff --git a/SRC/sgeqpf.f b/SRC/sgeqpf.f
index 23124882..1c631413 100644
--- a/SRC/sgeqpf.f
+++ b/SRC/sgeqpf.f
@@ -66,7 +66,7 @@
 *
 *  Each H(i) has the form
 *
-*     H = I - tau * v * v'
+*     H = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
diff --git a/SRC/sgeqr2.f b/SRC/sgeqr2.f
index 666015ff..e5fce4a9 100644
--- a/SRC/sgeqr2.f
+++ b/SRC/sgeqr2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
diff --git a/SRC/sgeqr2p.f b/SRC/sgeqr2p.f
index b2b91339..070e93b3 100644
--- a/SRC/sgeqr2p.f
+++ b/SRC/sgeqr2p.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
diff --git a/SRC/sgeqrf.f b/SRC/sgeqrf.f
index 203e7fb2..a2b71d80 100644
--- a/SRC/sgeqrf.f
+++ b/SRC/sgeqrf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**T to A(i:m,i+ib:n) from the left
 *
                CALL SLARFB( 'Left', 'Transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/sgeqrfp.f b/SRC/sgeqrfp.f
index 08f2c89d..6c6493fa 100644
--- a/SRC/sgeqrfp.f
+++ b/SRC/sgeqrfp.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL SLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**T to A(i:m,i+ib:n) from the left
 *
                CALL SLARFB( 'Left', 'Transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/sgerq2.f b/SRC/sgerq2.f
index ea4a1af6..3f6e5720 100644
--- a/SRC/sgerq2.f
+++ b/SRC/sgerq2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
diff --git a/SRC/sgerqf.f b/SRC/sgerqf.f
index 8f4a2686..639906ac 100644
--- a/SRC/sgerqf.f
+++ b/SRC/sgerqf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
diff --git a/SRC/sgetrs.f b/SRC/sgetrs.f
index 558e6e80..5aae04df 100644
--- a/SRC/sgetrs.f
+++ b/SRC/sgetrs.f
@@ -18,7 +18,7 @@
 *  =======
 *
 *  SGETRS solves a system of linear equations
-*     A * X = B  or  A' * X = B
+*     A * X = B  or  A**T * X = B
 *  with a general N-by-N matrix A using the LU factorization computed
 *  by SGETRF.
 *
@@ -28,8 +28,8 @@
 *  TRANS   (input) CHARACTER*1
 *          Specifies the form of the system of equations:
 *          = 'N':  A * X = B  (No transpose)
-*          = 'T':  A'* X = B  (Transpose)
-*          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
+*          = 'T':  A**T* X = B  (Transpose)
+*          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
 *
 *  N       (input) INTEGER
 *          The order of the matrix A.  N >= 0.
@@ -126,14 +126,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A' * X = B.
+*        Solve A**T * X = B.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B, overwriting B with X.
 *
          CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, overwriting B with X.
 *
          CALL STRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE,
      $               A, LDA, B, LDB )
diff --git a/SRC/sggglm.f b/SRC/sggglm.f
index a2b107d5..4b5eac46 100644
--- a/SRC/sggglm.f
+++ b/SRC/sggglm.f
@@ -186,9 +186,9 @@
 *
 *     Compute the GQR factorization of matrices A and B:
 *
-*            Q'*A = ( R11 ) M,    Q'*B*Z' = ( T11   T12 ) M
-*                   (  0  ) N-M             (  0    T22 ) N-M
-*                      M                     M+P-N  N-M
+*          Q**T*A = ( R11 ) M,    Q**T*B*Z**T = ( T11   T12 ) M
+*                   (  0  ) N-M                 (  0    T22 ) N-M
+*                      M                         M+P-N  N-M
 *
 *     where R11 and T22 are upper triangular, and Q and Z are
 *     orthogonal.
@@ -197,8 +197,8 @@
      $             WORK( M+NP+1 ), LWORK-M-NP, INFO )
       LOPT = WORK( M+NP+1 )
 *
-*     Update left-hand-side vector d = Q'*d = ( d1 ) M
-*                                             ( d2 ) N-M
+*     Update left-hand-side vector d = Q**T*d = ( d1 ) M
+*                                               ( d2 ) N-M
 *
       CALL SORMQR( 'Left', 'Transpose', N, 1, M, A, LDA, WORK, D,
      $             MAX( 1, N ), WORK( M+NP+1 ), LWORK-M-NP, INFO )
@@ -245,7 +245,7 @@
          CALL SCOPY( M, D, 1, X, 1 )
       END IF
 *
-*     Backward transformation y = Z'*y
+*     Backward transformation y = Z**T *y
 *
       CALL SORMRQ( 'Left', 'Transpose', P, 1, NP,
      $             B( MAX( 1, N-P+1 ), 1 ), LDB, WORK( M+1 ), Y,
diff --git a/SRC/sgglse.f b/SRC/sgglse.f
index e8e3b760..706853da 100644
--- a/SRC/sgglse.f
+++ b/SRC/sgglse.f
@@ -183,9 +183,9 @@
 *
 *     Compute the GRQ factorization of matrices B and A:
 *
-*            B*Q' = (  0  T12 ) P   Z'*A*Q' = ( R11 R12 ) N-P
-*                     N-P  P                  (  0  R22 ) M+P-N
-*                                               N-P  P
+*            B*Q**T = (  0  T12 ) P   Z**T*A*Q**T = ( R11 R12 ) N-P
+*                        N-P  P                     (  0  R22 ) M+P-N
+*                                                      N-P  P
 *
 *     where T12 and R11 are upper triangular, and Q and Z are
 *     orthogonal.
@@ -194,8 +194,8 @@
      $             WORK( P+MN+1 ), LWORK-P-MN, INFO )
       LOPT = WORK( P+MN+1 )
 *
-*     Update c = Z'*c = ( c1 ) N-P
-*                       ( c2 ) M+P-N
+*     Update c = Z**T *c = ( c1 ) N-P
+*                          ( c2 ) M+P-N
 *
       CALL SORMQR( 'Left', 'Transpose', M, 1, MN, A, LDA, WORK( P+1 ),
      $             C, MAX( 1, M ), WORK( P+MN+1 ), LWORK-P-MN, INFO )
@@ -233,7 +233,7 @@
             RETURN
          END IF
 *
-*        Put the solution in X
+*        Put the solutions in X
 *
          CALL SCOPY( N-P, C, 1, X, 1 )
       END IF
@@ -254,7 +254,7 @@
          CALL SAXPY( NR, -ONE, D, 1, C( N-P+1 ), 1 )
       END IF
 *
-*     Backward transformation x = Q'*x
+*     Backward transformation x = Q**T*x
 *
       CALL SORMRQ( 'Left', 'Transpose', N, 1, P, B, LDB, WORK( 1 ), X,
      $             N, WORK( P+MN+1 ), LWORK-P-MN, INFO )
diff --git a/SRC/sggqrf.f b/SRC/sggqrf.f
index 6f76c508..bb4f50f0 100644
--- a/SRC/sggqrf.f
+++ b/SRC/sggqrf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GQR factorization
 *  of A and B implicitly gives the QR factorization of inv(B)*A:
 *
-*               inv(B)*A = Z'*(inv(T)*R)
+*               inv(B)*A = Z**T*(inv(T)*R)
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
 *  transpose of the matrix Z.
 *
 *  Arguments
@@ -119,7 +119,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**T
 *
 *  where taua is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -133,7 +133,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**T
 *
 *  where taub is a real scalar, and v is a real vector with
 *  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
@@ -194,7 +194,7 @@
       CALL SGEQRF( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := Q'*B.
+*     Update B := Q**T*B.
 *
       CALL SORMQR( 'Left', 'Transpose', N, P, MIN( N, M ), A, LDA, TAUA,
      $             B, LDB, WORK, LWORK, INFO )
diff --git a/SRC/sggrqf.f b/SRC/sggrqf.f
index c752c7b0..aed20ed8 100644
--- a/SRC/sggrqf.f
+++ b/SRC/sggrqf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GRQ factorization
 *  of A and B implicitly gives the RQ factorization of A*inv(B):
 *
-*               A*inv(B) = (R*inv(T))*Z'
+*               A*inv(B) = (R*inv(T))*Z**T
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**T denotes the
 *  transpose of the matrix Z.
 *
 *  Arguments
@@ -118,7 +118,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**T
 *
 *  where taua is a real scalar, and v is a real vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
@@ -132,7 +132,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**T
 *
 *  where taub is a real scalar, and v is a real vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
@@ -193,7 +193,7 @@
       CALL SGERQF( M, N, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := B*Q'
+*     Update B := B*Q**T
 *
       CALL SORMRQ( 'Right', 'Transpose', P, N, MIN( M, N ),
      $             A( MAX( 1, M-N+1 ), 1 ), LDA, TAUA, B, LDB, WORK,
diff --git a/SRC/sggsvd.f b/SRC/sggsvd.f
index 65b0e7f9..61405d71 100644
--- a/SRC/sggsvd.f
+++ b/SRC/sggsvd.f
@@ -24,10 +24,10 @@
 *  SGGSVD computes the generalized singular value decomposition (GSVD)
 *  of an M-by-N real matrix A and P-by-N real matrix B:
 *
-*      U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R )
+*        U**T*A*Q = D1*( 0 R ),    V**T*B*Q = D2*( 0 R )
 *
-*  where U, V and Q are orthogonal matrices, and Z' is the transpose
-*  of Z.  Let K+L = the effective numerical rank of the matrix (A',B')',
+*  where U, V and Q are orthogonal matrices.
+*  Let K+L = the effective numerical rank of the matrix (A**T,B**T)**T,
 *  then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and
 *  D2 are M-by-(K+L) and P-by-(K+L) "diagonal" matrices and of the
 *  following structures, respectively:
@@ -86,13 +86,13 @@
 *
 *  In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
 *  A and B implicitly gives the SVD of A*inv(B):
-*                       A*inv(B) = U*(D1*inv(D2))*V'.
-*  If ( A',B')' has orthonormal columns, then the GSVD of A and B is
+*                       A*inv(B) = U*(D1*inv(D2))*V**T.
+*  If ( A**T,B**T)**T  has orthonormal columns, then the GSVD of A and B is
 *  also equal to the CS decomposition of A and B. Furthermore, the GSVD
 *  can be used to derive the solution of the eigenvalue problem:
-*                       A'*A x = lambda* B'*B x.
+*                       A**T*A x = lambda* B**T*B x.
 *  In some literature, the GSVD of A and B is presented in the form
-*                   U'*A*X = ( 0 D1 ),   V'*B*X = ( 0 D2 )
+*                   U**T*A*X = ( 0 D1 ),   V**T*B*X = ( 0 D2 )
 *  where U and V are orthogonal and X is nonsingular, D1 and D2 are
 *  ``diagonal''.  The former GSVD form can be converted to the latter
 *  form by taking the nonsingular matrix X as
@@ -128,7 +128,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in the Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A',B')**T.
 *
 *  A       (input/output) REAL array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
@@ -209,7 +209,7 @@
 *  TOLA    REAL
 *  TOLB    REAL
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')'. Generally, they are set to
+*          rank of (A',B')**T. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MACHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MACHEPS.
 *          The size of TOLA and TOLB may affect the size of backward
diff --git a/SRC/sggsvp.f b/SRC/sggsvp.f
index a62fbea5..4b633f30 100644
--- a/SRC/sggsvp.f
+++ b/SRC/sggsvp.f
@@ -23,24 +23,23 @@
 *
 *  SGGSVP computes orthogonal matrices U, V and Q such that
 *
-*                   N-K-L  K    L
-*   U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
-*                L ( 0     0   A23 )
-*            M-K-L ( 0     0    0  )
+*                     N-K-L  K    L
+*   U**T*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
+*                  L ( 0     0   A23 )
+*              M-K-L ( 0     0    0  )
 *
 *                   N-K-L  K    L
 *          =     K ( 0    A12  A13 )  if M-K-L < 0;
 *              M-K ( 0     0   A23 )
 *
-*                 N-K-L  K    L
-*   V'*B*Q =   L ( 0     0   B13 )
-*            P-L ( 0     0    0  )
+*                   N-K-L  K    L
+*   V**T*B*Q =   L ( 0     0   B13 )
+*              P-L ( 0     0    0  )
 *
 *  where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 *  upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 *  otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
-*  numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the
-*  transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -99,8 +98,8 @@
 *  K       (output) INTEGER
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
-*          described in Purpose.
-*          K + L = effective numerical rank of (A',B')'.
+*          described in Purpose section.
+*          K + L = effective numerical rank of (A**T,B**T)**T.
 *
 *  U       (output) REAL array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the orthogonal matrix U.
@@ -258,14 +257,14 @@
 *
          CALL SGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**T
 *
          CALL SORMR2( 'Right', 'Transpose', M, N, L, B, LDB, TAU, A,
      $                LDA, WORK, INFO )
 *
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**T
 *
             CALL SORMR2( 'Right', 'Transpose', N, N, L, B, LDB, TAU, Q,
      $                   LDQ, WORK, INFO )
@@ -287,7 +286,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**T
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -303,7 +302,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**T*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL SORM2R( 'Left', 'Transpose', M, L, MIN( M, N-L ), A, LDA,
      $             TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -345,7 +344,7 @@
 *
          IF( WANTQ ) THEN
 *
-*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1'
+*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**T
 *
             CALL SORMR2( 'Right', 'Transpose', N, N-L, K, A, LDA, TAU,
      $                   Q, LDQ, WORK, INFO )
diff --git a/SRC/sgtcon.f b/SRC/sgtcon.f
index 3d453942..53e8eb18 100644
--- a/SRC/sgtcon.f
+++ b/SRC/sgtcon.f
@@ -151,7 +151,7 @@
      $                   WORK, N, INFO )
          ELSE
 *
-*           Multiply by inv(L')*inv(U').
+*           Multiply by inv(L**T)*inv(U**T).
 *
             CALL SGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK,
      $                   N, INFO )
diff --git a/SRC/sgtsv.f b/SRC/sgtsv.f
index a8d77383..b2de9760 100644
--- a/SRC/sgtsv.f
+++ b/SRC/sgtsv.f
@@ -22,7 +22,7 @@
 *  where A is an n by n tridiagonal matrix, by Gaussian elimination with
 *  partial pivoting.
 *
-*  Note that the equation  A'*X = B  may be solved by interchanging the
+*  Note that the equation  A**T*X = B  may be solved by interchanging the
 *  order of the arguments DU and DL.
 *
 *  Arguments
diff --git a/SRC/sla_gbamv.f b/SRC/sla_gbamv.f
index f5fbfe1f..cab2aa11 100644
--- a/SRC/sla_gbamv.f
+++ b/SRC/sla_gbamv.f
@@ -25,7 +25,7 @@
 *  SLA_GBAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -47,43 +47,43 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  KL      (input) INTEGER
+*  KL       (input) INTEGER
 *           The number of subdiagonals within the band of A.  KL >= 0.
 *
-*  KU      (input) INTEGER
+*  KU       (input) INTEGER
 *           The number of superdiagonals within the band of A.  KU >= 0.
 *
-*  ALPHA   (input) REAL
+*  ALPHA    (input) REAL
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - REAL             array of DIMENSION ( LDA, n )
-*           Before entry, the leading m by n part of the array A must
+*  AB       (input) REAL array of DIMENSION ( LDAB, n )
+*           Before entry, the leading m by n part of the array AB must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
-*           On entry, LDA specifies the first dimension of A as declared
-*           in the calling (sub) program. LDA must be at least
+*  LDAB     (input) INTEGER
+*           On entry, LDA specifies the first dimension of AB as declared
+*           in the calling (sub) program. LDAB must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) REAL array, dimension
+*  X        (input) REAL array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -91,17 +91,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA    (input) REAL
+*  BETA     (input)  REAL
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y       (input/output) REAL array, dimension
+*  Y        (input/output) REAL  array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -109,7 +109,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/sla_geamv.f b/SRC/sla_geamv.f
index ca9e1bad..29681994 100644
--- a/SRC/sla_geamv.f
+++ b/SRC/sla_geamv.f
@@ -25,7 +25,7 @@
 *  SLA_GEAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -47,37 +47,37 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  ALPHA   (input) REAL
+*  ALPHA    (input) REAL
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - REAL             array of DIMENSION ( LDA, n )
+*  A        (input) REAL array of DIMENSION ( LDA, n )
 *           Before entry, the leading m by n part of the array A must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
+*  LDA      (input) INTEGER
 *           On entry, LDA specifies the first dimension of A as declared
 *           in the calling (sub) program. LDA must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) REAL array, dimension
+*  X        (input) REAL array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -85,17 +85,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA    (input) REAL
+*  BETA     (input) REAL
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y      - REAL
+*  Y        (input/output) REAL
 *           Array of DIMENSION at least
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
@@ -104,7 +104,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/slabrd.f b/SRC/slabrd.f
index 5a1b2225..a4e3a7ae 100644
--- a/SRC/slabrd.f
+++ b/SRC/slabrd.f
@@ -19,7 +19,7 @@
 *
 *  SLABRD reduces the first NB rows and columns of a real general
 *  m by n matrix A to upper or lower bidiagonal form by an orthogonal
-*  transformation Q' * A * P, and returns the matrices X and Y which
+*  transformation Q**T * A * P, and returns the matrices X and Y which
 *  are needed to apply the transformation to the unreduced part of A.
 *
 *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
@@ -81,14 +81,14 @@
 *          of A.
 *
 *  LDX     (input) INTEGER
-*          The leading dimension of the array X. LDX >= M.
+*          The leading dimension of the array X. LDX >= max(1,M).
 *
 *  Y       (output) REAL array, dimension (LDY,NB)
 *          The n-by-nb matrix Y required to update the unreduced part
 *          of A.
 *
 *  LDY     (input) INTEGER
-*          The leading dimension of the array Y. LDY >= N.
+*          The leading dimension of the array Y. LDY >= max(1,N).
 *
 *  Further Details
 *  ===============
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
 *
 *  where tauq and taup are real scalars, and v and u are real vectors.
 *
@@ -113,9 +113,9 @@
 *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  The elements of the vectors v and u together form the m-by-nb matrix
-*  V and the nb-by-n matrix U' which are needed, with X and Y, to apply
+*  V and the nb-by-n matrix U**T which are needed, with X and Y, to apply
 *  the transformation to the unreduced part of the matrix, using a block
-*  update of the form:  A := A - V*Y' - X*U'.
+*  update of the form:  A := A - V*Y**T - X*U**T.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with nb = 2:
diff --git a/SRC/slaed7.f b/SRC/slaed7.f
index 98ca6813..b0fd20eb 100644
--- a/SRC/slaed7.f
+++ b/SRC/slaed7.f
@@ -31,9 +31,9 @@
 *  the case in which all eigenvalues and eigenvectors of a symmetric
 *  tridiagonal matrix are desired.
 *
-*    T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
+*    T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
 *
-*     where Z = Q'u, u is a vector of length N with ones in the
+*     where Z = Q**Tu, u is a vector of length N with ones in the
 *     CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
 *
 *     The eigenvectors of the original matrix are stored in Q, and the
diff --git a/SRC/slaein.f b/SRC/slaein.f
index b43fed4f..557d20cb 100644
--- a/SRC/slaein.f
+++ b/SRC/slaein.f
@@ -232,7 +232,7 @@
          DO 110 ITS = 1, N
 *
 *           Solve U*x = scale*v for a right eigenvector
-*             or U'*x = scale*v for a left eigenvector,
+*             or U**T*x = scale*v for a left eigenvector,
 *           overwriting x on v.
 *
             CALL SLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB,
diff --git a/SRC/slags2.f b/SRC/slags2.f
index da34ecc6..e2b854c3 100644
--- a/SRC/slags2.f
+++ b/SRC/slags2.f
@@ -18,19 +18,19 @@
 *  SLAGS2 computes 2-by-2 orthogonal matrices U, V and Q, such
 *  that if ( UPPER ) then
 *
-*            U'*A*Q = U'*( A1 A2 )*Q = ( x  0  )
-*                        ( 0  A3 )     ( x  x  )
+*            U**T *A*Q = U**T *( A1 A2 )*Q = ( x  0  )
+*                              ( 0  A3 )     ( x  x  )
 *  and
-*            V'*B*Q = V'*( B1 B2 )*Q = ( x  0  )
-*                        ( 0  B3 )     ( x  x  )
+*            V**T*B*Q = V**T *( B1 B2 )*Q = ( x  0  )
+*                             ( 0  B3 )     ( x  x  )
 *
 *  or if ( .NOT.UPPER ) then
 *
-*            U'*A*Q = U'*( A1 0  )*Q = ( x  x  )
-*                        ( A2 A3 )     ( 0  x  )
+*            U**T *A*Q = U**T *( A1 0  )*Q = ( x  x  )
+*                              ( A2 A3 )     ( 0  x  )
 *  and
-*            V'*B*Q = V'*( B1 0  )*Q = ( x  x  )
-*                        ( B2 B3 )     ( 0  x  )
+*            V**T*B*Q = V**T*( B1 0  )*Q = ( x  x  )
+*                            ( B2 B3 )     ( 0  x  )
 *
 *  The rows of the transformed A and B are parallel, where
 *
@@ -112,8 +112,8 @@
          IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
      $        THEN
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11R = CSL*A1
             UA12 = CSL*A2 + SNL*A3
@@ -124,7 +124,7 @@
             AUA12 = ABS( CSL )*ABS( A2 ) + ABS( SNL )*ABS( A3 )
             AVB12 = ABS( CSR )*ABS( B2 ) + ABS( SNR )*ABS( B3 )
 *
-*           zero (1,2) elements of U'*A and V'*B
+*           zero (1,2) elements of U**T *A and V**T *B
 *
             IF( ( ABS( UA11R )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA12 / ( ABS( UA11R )+ABS( UA12 ) ).LE.AVB12 /
@@ -144,8 +144,8 @@
 *
          ELSE
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,2) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNL*A1
             UA22 = -SNL*A2 + CSL*A3
@@ -156,7 +156,7 @@
             AUA22 = ABS( SNL )*ABS( A2 ) + ABS( CSL )*ABS( A3 )
             AVB22 = ABS( SNR )*ABS( B2 ) + ABS( CSR )*ABS( B3 )
 *
-*           zero (2,2) elements of U'*A and V'*B, and then swap.
+*           zero (2,2) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA21 )+ABS( UA22 ) ).NE.ZERO ) THEN
                IF( AUA22 / ( ABS( UA21 )+ABS( UA22 ) ).LE.AVB22 /
@@ -197,8 +197,8 @@
          IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) )
      $        THEN
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**T *A and V**T *B,
+*           and (2,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA21 = -SNR*A1 + CSR*A2
             UA22R = CSR*A3
@@ -209,7 +209,7 @@
             AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS( A2 )
             AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS( B2 )
 *
-*           zero (2,1) elements of U'*A and V'*B.
+*           zero (2,1) elements of U**T *A and V**T *B.
 *
             IF( ( ABS( UA21 )+ABS( UA22R ) ).NE.ZERO ) THEN
                IF( AUA21 / ( ABS( UA21 )+ABS( UA22R ) ).LE.AVB21 /
@@ -229,8 +229,8 @@
 *
          ELSE
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**T *A and V**T *B,
+*           and (1,1) element of |U|**T *|A| and |V|**T *|B|.
 *
             UA11 = CSR*A1 + SNR*A2
             UA12 = SNR*A3
@@ -241,7 +241,7 @@
             AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS( A2 )
             AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS( B2 )
 *
-*           zero (1,1) elements of U'*A and V'*B, and then swap.
+*           zero (1,1) elements of U**T*A and V**T*B, and then swap.
 *
             IF( ( ABS( UA11 )+ABS( UA12 ) ).NE.ZERO ) THEN
                IF( AUA11 / ( ABS( UA11 )+ABS( UA12 ) ).LE.AVB11 /
diff --git a/SRC/slagtm.f b/SRC/slagtm.f
index a91fbdd8..fe96b309 100644
--- a/SRC/slagtm.f
+++ b/SRC/slagtm.f
@@ -128,7 +128,7 @@
    60       CONTINUE
          ELSE
 *
-*           Compute B := B + A'*X
+*           Compute B := B + A**T*X
 *
             DO 80 J = 1, NRHS
                IF( N.EQ.1 ) THEN
@@ -166,7 +166,7 @@
   100       CONTINUE
          ELSE
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**T*X
 *
             DO 120 J = 1, NRHS
                IF( N.EQ.1 ) THEN
diff --git a/SRC/slagts.f b/SRC/slagts.f
index 619a4e2c..16e95380 100644
--- a/SRC/slagts.f
+++ b/SRC/slagts.f
@@ -19,7 +19,7 @@
 *
 *  SLAGTS may be used to solve one of the systems of equations
 *
-*     (T - lambda*I)*x = y   or   (T - lambda*I)'*x = y,
+*     (T - lambda*I)*x = y   or   (T - lambda*I)**T*x = y,
 *
 *  where T is an n by n tridiagonal matrix, for x, following the
 *  factorization of (T - lambda*I) as
@@ -42,9 +42,9 @@
 *                and, if overflow would otherwise occur, the diagonal
 *                elements of U are to be perturbed. See argument TOL
 *                below.
-*          =  2: The equations  (T - lambda*I)'x = y  are to be solved,
+*          =  2: The equations  (T - lambda*I)**Tx = y  are to be solved,
 *                but diagonal elements of U are not to be perturbed.
-*          = -2: The equations  (T - lambda*I)'x = y  are to be solved
+*          = -2: The equations  (T - lambda*I)**Tx = y  are to be solved
 *                and, if overflow would otherwise occur, the diagonal
 *                elements of U are to be perturbed. See argument TOL
 *                below.
diff --git a/SRC/slahr2.f b/SRC/slahr2.f
index 2a9d2641..1d63053a 100644
--- a/SRC/slahr2.f
+++ b/SRC/slahr2.f
@@ -19,8 +19,8 @@
 *  SLAHR2 reduces the first NB columns of A real general n-BY-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an orthogonal similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**T * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
 *
 *  This is an auxiliary routine called by SGEHRD.
 *
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -84,7 +84,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**T) * (A - Y*V**T).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -144,12 +144,12 @@
 *
 *           Update A(K+1:N,I)
 *
-*           Update I-th column of A - Y * V'
+*           Update I-th column of A - Y * V**T
 *
             CALL SGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T' * V**T to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -164,13 +164,13 @@
      $                  I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**T * b2
 *
             CALL SGEMV( 'Transpose', N-K-I+1, I-1, 
      $                  ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**T * w
 *
             CALL STRMV( 'Upper', 'Transpose', 'NON-UNIT', 
      $                  I-1, T, LDT,
diff --git a/SRC/slahrd.f b/SRC/slahrd.f
index fc6d5a18..9c995463 100644
--- a/SRC/slahrd.f
+++ b/SRC/slahrd.f
@@ -19,8 +19,8 @@
 *  SLAHRD reduces the first NB columns of a real general n-by-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an orthogonal similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**T * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**T, and also the matrix Y = A * V * T.
 *
 *  This is an OBSOLETE auxiliary routine. 
 *  This routine will be 'deprecated' in a  future release.
@@ -76,7 +76,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -85,7 +85,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**T) * (A - Y*V**T).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -130,12 +130,12 @@
 *
 *           Update A(1:n,i)
 *
-*           Compute i-th column of A - Y * V'
+*           Compute i-th column of A - Y * V**T
 *
             CALL SGEMV( 'No transpose', N, I-1, -ONE, Y, LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( 1, I ), 1 )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T**T * V**T to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -143,18 +143,18 @@
 *
 *           where V1 is unit lower triangular
 *
-*           w := V1' * b1
+*           w := V1**T * b1
 *
             CALL SCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
             CALL STRMV( 'Lower', 'Transpose', 'Unit', I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**T *b2
 *
             CALL SGEMV( 'Transpose', N-K-I+1, I-1, ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**T *w
 *
             CALL STRMV( 'Upper', 'Transpose', 'Non-unit', I-1, T, LDT,
      $                  T( 1, NB ), 1 )
diff --git a/SRC/slaic1.f b/SRC/slaic1.f
index fb3a94e9..ab4680a8 100644
--- a/SRC/slaic1.f
+++ b/SRC/slaic1.f
@@ -40,7 +40,7 @@
 *      diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
 *                                            [ gamma ]
 *
-*  where  alpha =  x'*w.
+*  where  alpha =  x**T*w.
 *
 *  Arguments
 *  =========
diff --git a/SRC/slaqp2.f b/SRC/slaqp2.f
index 337ddc69..d838c8fa 100644
--- a/SRC/slaqp2.f
+++ b/SRC/slaqp2.f
@@ -133,7 +133,7 @@
 *
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(offset+i:m,i+1:n) from the left.
+*           Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
 *
             AII = A( OFFPI, I )
             A( OFFPI, I ) = ONE
diff --git a/SRC/slaqps.f b/SRC/slaqps.f
index f251cabc..ed99d005 100644
--- a/SRC/slaqps.f
+++ b/SRC/slaqps.f
@@ -142,7 +142,7 @@
          END IF
 *
 *        Apply previous Householder reflectors to column K:
-*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
+*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T.
 *
          IF( K.GT.1 ) THEN
             CALL SGEMV( 'No transpose', M-RK+1, K-1, -ONE, A( RK, 1 ),
@@ -162,7 +162,7 @@
 *
 *        Compute Kth column of F:
 *
-*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
+*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K).
 *
          IF( K.LT.N ) THEN
             CALL SGEMV( 'Transpose', M-RK+1, N-K, TAU( K ),
@@ -177,7 +177,7 @@
    20    CONTINUE
 *
 *        Incremental updating of F:
-*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
+*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T
 *                    *A(RK:M,K).
 *
          IF( K.GT.1 ) THEN
@@ -189,7 +189,7 @@
          END IF
 *
 *        Update the current row of A:
-*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
+*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T.
 *
          IF( K.LT.N ) THEN
             CALL SGEMV( 'No transpose', N-K, K, -ONE, F( K+1, 1 ), LDF,
@@ -229,7 +229,7 @@
 *
 *     Apply the block reflector to the rest of the matrix:
 *     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
-*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
+*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T.
 *
       IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
          CALL SGEMM( 'No transpose', 'Transpose', M-RK, N-KB, KB, -ONE,
diff --git a/SRC/slaqsb.f b/SRC/slaqsb.f
index 14647a7b..d693fab9 100644
--- a/SRC/slaqsb.f
+++ b/SRC/slaqsb.f
@@ -45,7 +45,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T*U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/slaqtr.f b/SRC/slaqtr.f
index 52a40270..46843f02 100644
--- a/SRC/slaqtr.f
+++ b/SRC/slaqtr.f
@@ -51,7 +51,7 @@
 *  LTRAN   (input) LOGICAL
 *          On entry, LTRAN specifies the option of conjugate transpose:
 *             = .FALSE.,    op(T+i*B) = T+i*B,
-*             = .TRUE.,     op(T+i*B) = (T+i*B)'.
+*             = .TRUE.,     op(T+i*B) = (T+i*B)**T.
 *
 *  LREAL   (input) LOGICAL
 *          On entry, LREAL specifies the input matrix structure:
@@ -532,7 +532,7 @@
 *
          ELSE
 *
-*           Solve (T + iB)'*(p+iq) = c+id
+*           Solve (T + iB)**T*(p+iq) = c+id
 *
             JNEXT = 1
             DO 80 J = 1, N
diff --git a/SRC/slar1v.f b/SRC/slar1v.f
index 19287c6d..1c059ed0 100644
--- a/SRC/slar1v.f
+++ b/SRC/slar1v.f
@@ -25,14 +25,14 @@
 *
 *  SLAR1V computes the (scaled) r-th column of the inverse of
 *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix
-*  L D L^T - sigma I. When sigma is close to an eigenvalue, the
+*  L D L**T - sigma I. When sigma is close to an eigenvalue, the
 *  computed vector is an accurate eigenvector. Usually, r corresponds
 *  to the index where the eigenvector is largest in magnitude.
 *  The following steps accomplish this computation :
-*  (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T,
-*  (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T,
+*  (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
+*  (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
 *  (c) Computation of the diagonal elements of the inverse of
-*      L D L^T - sigma I by combining the above transforms, and choosing
+*      L D L**T - sigma I by combining the above transforms, and choosing
 *      r as the index where the diagonal of the inverse is (one of the)
 *      largest in magnitude.
 *  (d) Computation of the (scaled) r-th column of the inverse using the
@@ -43,40 +43,40 @@
 *  =========
 *
 *  N        (input) INTEGER
-*           The order of the matrix L D L^T.
+*           The order of the matrix L D L**T.
 *
 *  B1       (input) INTEGER
-*           First index of the submatrix of L D L^T.
+*           First index of the submatrix of L D L**T.
 *
 *  BN       (input) INTEGER
-*           Last index of the submatrix of L D L^T.
+*           Last index of the submatrix of L D L**T.
 *
-*  LAMBDA    (input) REAL            
+*  LAMBDA    (input) REAL
 *           The shift. In order to compute an accurate eigenvector,
 *           LAMBDA should be a good approximation to an eigenvalue
-*           of L D L^T.
+*           of L D L**T.
 *
-*  L        (input) REAL             array, dimension (N-1)
+*  L        (input) REAL array, dimension (N-1)
 *           The (n-1) subdiagonal elements of the unit bidiagonal matrix
 *           L, in elements 1 to N-1.
 *
-*  D        (input) REAL             array, dimension (N)
+*  D        (input) REAL array, dimension (N)
 *           The n diagonal elements of the diagonal matrix D.
 *
-*  LD       (input) REAL             array, dimension (N-1)
+*  LD       (input) REAL array, dimension (N-1)
 *           The n-1 elements L(i)*D(i).
 *
-*  LLD      (input) REAL             array, dimension (N-1)
+*  LLD      (input) REAL array, dimension (N-1)
 *           The n-1 elements L(i)*L(i)*D(i).
 *
-*  PIVMIN   (input) REAL            
+*  PIVMIN   (input) REAL
 *           The minimum pivot in the Sturm sequence.
 *
-*  GAPTOL   (input) REAL            
+*  GAPTOL   (input) REAL
 *           Tolerance that indicates when eigenvector entries are negligible
 *           w.r.t. their contribution to the residual.
 *
-*  Z        (input/output) REAL             array, dimension (N)
+*  Z        (input/output) REAL array, dimension (N)
 *           On input, all entries of Z must be set to 0.
 *           On output, Z contains the (scaled) r-th column of the
 *           inverse. The scaling is such that Z(R) equals 1.
@@ -86,20 +86,20 @@
 *
 *  NEGCNT   (output) INTEGER
 *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
-*           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.
+*           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.
 *
-*  ZTZ      (output) REAL            
+*  ZTZ      (output) REAL
 *           The square of the 2-norm of Z.
 *
-*  MINGMA   (output) REAL            
+*  MINGMA   (output) REAL
 *           The reciprocal of the largest (in magnitude) diagonal
-*           element of the inverse of L D L^T - sigma I.
+*           element of the inverse of L D L**T - sigma I.
 *
 *  R        (input/output) INTEGER
 *           The twist index for the twisted factorization used to
 *           compute Z.
 *           On input, 0 <= R <= N. If R is input as 0, R is set to
-*           the index where (L D L^T - sigma I)^{-1} is largest
+*           the index where (L D L**T - sigma I)^{-1} is largest
 *           in magnitude. If 1 <= R <= N, R is unchanged.
 *           On output, R contains the twist index used to compute Z.
 *           Ideally, R designates the position of the maximum entry in the
@@ -109,18 +109,18 @@
 *           The support of the vector in Z, i.e., the vector Z is
 *           nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ).
 *
-*  NRMINV   (output) REAL            
+*  NRMINV   (output) REAL
 *           NRMINV = 1/SQRT( ZTZ )
 *
-*  RESID    (output) REAL            
+*  RESID    (output) REAL
 *           The residual of the FP vector.
 *           RESID = ABS( MINGMA )/SQRT( ZTZ )
 *
-*  RQCORR   (output) REAL            
+*  RQCORR   (output) REAL
 *           The Rayleigh Quotient correction to LAMBDA.
 *           RQCORR = MINGMA*TMP
 *
-*  WORK     (workspace) REAL             array, dimension (4*N)
+*  WORK     (workspace) REAL array, dimension (4*N)
 *
 *  Further Details
 *  ===============
diff --git a/SRC/slarf.f b/SRC/slarf.f
index b1e1539b..380d808b 100644
--- a/SRC/slarf.f
+++ b/SRC/slarf.f
@@ -21,7 +21,7 @@
 *  SLARF applies a real elementary reflector H to a real m by n matrix
 *  C, from either the left or the right. H is represented in the form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
@@ -121,12 +121,12 @@
 *
          IF( LASTV.GT.0 ) THEN
 *
-*           w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)
+*           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
 *
             CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
      $           ZERO, WORK, 1 )
 *
-*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'
+*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
 *
             CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
          END IF
@@ -141,7 +141,7 @@
             CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
      $           V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'
+*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
 *
             CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
          END IF
diff --git a/SRC/slarfb.f b/SRC/slarfb.f
index a4f23c17..597aaafe 100644
--- a/SRC/slarfb.f
+++ b/SRC/slarfb.f
@@ -19,19 +19,19 @@
 *  Purpose
 *  =======
 *
-*  SLARFB applies a real block reflector H or its transpose H' to a
+*  SLARFB applies a real block reflector H or its transpose H**T to a
 *  real m by n matrix C, from either the left or the right.
 *
 *  Arguments
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**T from the Left
+*          = 'R': apply H or H**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'T': apply H' (Transpose)
+*          = 'T': apply H**T (Transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -76,10 +76,10 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
 *
 *  LDC     (input) INTEGER
-*          The leading dimension of the array C. LDA >= max(1,M).
+*          The leading dimension of the array C. LDC >= max(1,M).
 *
 *  WORK    (workspace) REAL array, dimension (LDWORK,K)
 *
@@ -154,15 +154,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILASLR( M, K, V, LDV ) )
                LASTC = ILASLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C**T * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
-*              W := C1'
+*              W := C1**T
 *
                DO 10 J = 1, K
                   CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
@@ -174,7 +174,7 @@
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2
+*                 W := W + C2**T *V2
 *
                   CALL SGEMM( 'Transpose', 'No transpose',
      $                 LASTC, K, LASTV-K,
@@ -182,16 +182,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2 * W'
+*                 C2 := C2 - V2 * W**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTV-K, LASTC, K,
@@ -199,12 +199,12 @@
      $                 C( K+1, 1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**T
 *
                DO 30 J = 1, K
                   DO 20 I = 1, LASTC
@@ -214,7 +214,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILASLR( N, K, V, LDV ) )
                LASTC = ILASLR( M, LASTV, C, LDC )
@@ -241,16 +241,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - W * V2'
+*                 C2 := C2 - W * V2**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTC, LASTV-K, K,
@@ -258,7 +258,7 @@
      $                 C( 1, K+1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
@@ -280,15 +280,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILASLR( M, K, V, LDV ) )
                LASTC = ILASLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C' * V  =  (C1**T * V1 + C2**T * V2)  (stored in WORK)
 *
-*              W := C2'
+*              W := C2**T
 *
                DO 70 J = 1, K
                   CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -302,36 +302,36 @@
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1
+*                 W := W + C1**T*V1
 *
                   CALL SGEMM( 'Transpose', 'No transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1 * W'
+*                 C1 := C1 - V1 * W**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**T
 *
                DO 90 J = 1, K
                   DO 80 I = 1, LASTC
@@ -341,7 +341,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILASLR( N, K, V, LDV ) )
                LASTC = ILASLR( M, LASTV, C, LDC )
@@ -368,7 +368,7 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -377,14 +377,14 @@
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - W * V1'
+*                 C1 := C1 - W * V1**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
@@ -409,27 +409,27 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILASLC( K, M, V, LDV ) )
                LASTC = ILASLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
-*              W := C1'
+*              W := C1**T
 *
                DO 130 J = 1, K
                   CALL SCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
   130          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2'
+*                 W := W + C2**T*V2**T
 *
                   CALL SGEMM( 'Transpose', 'Transpose',
      $                 LASTC, K, LASTV-K,
@@ -437,16 +437,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL STRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**T * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2' * W'
+*                 C2 := C2 - V2**T * W**T
 *
                   CALL SGEMM( 'Transpose', 'Transpose',
      $                 LASTV-K, LASTC, K,
@@ -459,7 +459,7 @@
                CALL STRMM( 'Right', 'Upper', 'No transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**T
 *
                DO 150 J = 1, K
                   DO 140 I = 1, LASTC
@@ -469,12 +469,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILASLC( K, N, V, LDV ) )
                LASTC = ILASLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C1
 *
@@ -482,13 +482,13 @@
                   CALL SCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**T
 *
                CALL STRMM( 'Right', 'Upper', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2 * V2'
+*                 W := W + C2 * V2**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTC, K, LASTV-K,
@@ -496,7 +496,7 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL STRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -535,45 +535,45 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**T * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILASLC( K, M, V, LDV ) )
                LASTC = ILASLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**T * V**T  =  (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
 *
-*              W := C2'
+*              W := C2**T
 *
                DO 190 J = 1, K
                   CALL SCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
      $                 WORK( 1, J ), 1 )
   190          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1'
+*                 W := W + C1**T * V1**T
 *
                   CALL SGEMM( 'Transpose', 'Transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**T  or  W * T
 *
                CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**T * W**T
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1' * W'
+*                 C1 := C1 - V1**T * W**T
 *
                   CALL SGEMM( 'Transpose', 'Transpose',
      $                 LASTV-K, LASTC, K, -ONE, V, LDV, WORK, LDWORK,
@@ -586,7 +586,7 @@
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**T
 *
                DO 210 J = 1, K
                   DO 200 I = 1, LASTC
@@ -596,12 +596,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**T  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILASLC( K, N, V, LDV ) )
                LASTC = ILASLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**T  =  (C1*V1**T + C2*V2**T)  (stored in WORK)
 *
 *              W := C2
 *
@@ -610,21 +610,21 @@
      $                 WORK( 1, J ), 1 )
   220          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**T
 *
                CALL STRMM( 'Right', 'Lower', 'Transpose', 'Unit',
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1 * V1'
+*                 W := W + C1 * V1**T
 *
                   CALL SGEMM( 'No transpose', 'Transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV,
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**T
 *
                CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
diff --git a/SRC/slarfg.f b/SRC/slarfg.f
index 9da24ab3..8afa18d5 100644
--- a/SRC/slarfg.f
+++ b/SRC/slarfg.f
@@ -19,13 +19,13 @@
 *  SLARFG generates a real elementary reflector H of order n, such
 *  that
 *
-*        H * ( alpha ) = ( beta ),   H' * H = I.
+*        H * ( alpha ) = ( beta ),   H**T * H = I.
 *            (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, and x is an (n-1)-element real
 *  vector. H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**T ) ,
 *                      ( v )
 *
 *  where tau is a real scalar and v is a real (n-1)-element
diff --git a/SRC/slarfgp.f b/SRC/slarfgp.f
index 5b08c067..14f61349 100644
--- a/SRC/slarfgp.f
+++ b/SRC/slarfgp.f
@@ -19,13 +19,13 @@
 *  SLARFGP generates a real elementary reflector H of order n, such
 *  that
 *
-*        H * ( alpha ) = ( beta ),   H' * H = I.
+*        H * ( alpha ) = ( beta ),   H**T * H = I.
 *            (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, beta is non-negative, and x is
 *  an (n-1)-element real vector.  H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**T ) ,
 *                      ( v )
 *
 *  where tau is a real scalar and v is a real (n-1)-element
diff --git a/SRC/slarft.f b/SRC/slarft.f
index f4eaab07..d2801834 100644
--- a/SRC/slarft.f
+++ b/SRC/slarft.f
@@ -27,12 +27,12 @@
 *  If STOREV = 'C', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th column of the array V, and
 *
-*     H  =  I - V * T * V'
+*     H  =  I - V * T * V**T
 *
 *  If STOREV = 'R', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th row of the array V, and
 *
-*     H  =  I - V' * T * V
+*     H  =  I - V**T * T * V
 *
 *  Arguments
 *  =========
@@ -150,7 +150,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i)
+*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**T * V(i:j,i)
 *
                   CALL SGEMV( 'Transpose', J-I+1, I-1, -TAU( I ),
      $                        V( I, 1 ), LDV, V( I, I ), 1, ZERO,
@@ -162,7 +162,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)'
+*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**T
 *
                   CALL SGEMV( 'No transpose', I-1, J-I+1, -TAU( I ),
      $                        V( 1, I ), LDV, V( I, I ), LDV, ZERO,
@@ -207,7 +207,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i)
+*                            - tau(i) * V(j:n-k+i,i+1:k)**T * V(j:n-k+i,i)
 *
                      CALL SGEMV( 'Transpose', N-K+I-J+1, K-I, -TAU( I ),
      $                           V( J, I+1 ), LDV, V( J, I ), 1, ZERO,
@@ -223,7 +223,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)'
+*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**T
 *
                      CALL SGEMV( 'No transpose', K-I, N-K+I-J+1,
      $                    -TAU( I ), V( I+1, J ), LDV, V( I, J ), LDV,
diff --git a/SRC/slarfx.f b/SRC/slarfx.f
index e2279897..3af7f92b 100644
--- a/SRC/slarfx.f
+++ b/SRC/slarfx.f
@@ -21,7 +21,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
diff --git a/SRC/slarrv.f b/SRC/slarrv.f
index a59cd945..aa60876e 100644
--- a/SRC/slarrv.f
+++ b/SRC/slarrv.f
@@ -25,7 +25,7 @@
 *  =======
 *
 *  SLARRV computes the eigenvectors of the tridiagonal matrix
-*  T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T.
+*  T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
 *  The input eigenvalues should have been computed by SLARRE.
 *
 *  Arguments
diff --git a/SRC/slarz.f b/SRC/slarz.f
index 22ab06f9..f842ee01 100644
--- a/SRC/slarz.f
+++ b/SRC/slarz.f
@@ -21,7 +21,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**T
 *
 *  where tau is a real scalar and v is a real vector.
 *
@@ -101,7 +101,7 @@
 *
             CALL SCOPY( N, C, LDC, WORK, 1 )
 *
-*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
+*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
 *
             CALL SGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
      $                  INCV, ONE, WORK, 1 )
@@ -111,7 +111,7 @@
             CALL SAXPY( N, -TAU, WORK, 1, C, LDC )
 *
 *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                               tau * v( 1:l ) * w( 1:n )'
+*                               tau * v( 1:l ) * w( 1:n )**T
 *
             CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
      $                 LDC )
@@ -137,7 +137,7 @@
             CALL SAXPY( M, -TAU, WORK, 1, C, 1 )
 *
 *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
-*                               tau * w( 1:m ) * v( 1:l )'
+*                               tau * w( 1:m ) * v( 1:l )**T
 *
             CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
      $                 LDC )
diff --git a/SRC/slarzb.f b/SRC/slarzb.f
index fcd26c86..1c335cc8 100644
--- a/SRC/slarzb.f
+++ b/SRC/slarzb.f
@@ -27,12 +27,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**T from the Left
+*          = 'R': apply H or H**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Transpose)
+*          = 'C': apply H**T (Transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -77,7 +77,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -140,16 +140,16 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        Form  H * C  or  H' * C
+*        Form  H * C  or  H**T * C
 *
-*        W( 1:n, 1:k ) = C( 1:k, 1:n )'
+*        W( 1:n, 1:k ) = C( 1:k, 1:n )**T
 *
          DO 10 J = 1, K
             CALL SCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10    CONTINUE
 *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
-*                        C( m-l+1:m, 1:n )' * V( 1:k, 1:l )'
+*                        C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL SGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
@@ -160,7 +160,7 @@
          CALL STRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
      $               LDT, WORK, LDWORK )
 *
-*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )'
+*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
 *
          DO 30 J = 1, N
             DO 20 I = 1, K
@@ -169,7 +169,7 @@
    30    CONTINUE
 *
 *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                            V( 1:k, 1:l )' * W( 1:n, 1:k )'
+*                            V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
 *
          IF( L.GT.0 )
      $      CALL SGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
@@ -177,7 +177,7 @@
 *
       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*        Form  C * H  or  C * H'
+*        Form  C * H  or  C * H**T
 *
 *        W( 1:m, 1:k ) = C( 1:m, 1:k )
 *
@@ -186,13 +186,13 @@
    40    CONTINUE
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
-*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )'
+*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL SGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
      $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *
-*        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T'
+*        W( 1:m, 1:k ) = W( 1:m, 1:k ) * T  or  W( 1:m, 1:k ) * T**T
 *
          CALL STRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
      $               LDT, WORK, LDWORK )
diff --git a/SRC/slarzt.f b/SRC/slarzt.f
index a30ecb1b..077ee709 100644
--- a/SRC/slarzt.f
+++ b/SRC/slarzt.f
@@ -164,7 +164,7 @@
 *
             IF( I.LT.K ) THEN
 *
-*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
+*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**T
 *
                CALL SGEMV( 'No transpose', K-I, N, -TAU( I ),
      $                     V( I+1, 1 ), LDV, V( I, 1 ), LDV, ZERO,
diff --git a/SRC/slasd1.f b/SRC/slasd1.f
index b76a6fd7..4fae39ae 100644
--- a/SRC/slasd1.f
+++ b/SRC/slasd1.f
@@ -98,8 +98,8 @@
 *
 *  VT     (input/output) REAL array, dimension (LDVT,M)
 *         where M = N + SQRE.
-*         On entry VT(1:NL+1, 1:NL+1)' contains the right singular
-*         vectors of the upper block; VT(NL+2:M, NL+2:M)' contains
+*         On entry VT(1:NL+1, 1:NL+1)**T contains the right singular
+*         vectors of the upper block; VT(NL+2:M, NL+2:M)**T contains
 *         the right singular vectors of the lower block. On exit
 *         VT' contains the right singular vectors of the
 *         bidiagonal matrix.
diff --git a/SRC/slasyf.f b/SRC/slasyf.f
index 71d7ab04..b9053885 100644
--- a/SRC/slasyf.f
+++ b/SRC/slasyf.f
@@ -21,11 +21,11 @@
 *  using the Bunch-Kaufman diagonal pivoting method. The partial
 *  factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
 *
-*  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) (  0  A22 ) (  0    I   )
+*  A  =  ( L11  0 ) (  D   0  ) ( L11**T L21**T )  if UPLO = 'L'
+*        ( L21  I ) (  0  A22 ) (  0       I    )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
@@ -313,7 +313,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
 *
 *        computing blocks of NB columns at a time
 *
@@ -536,7 +536,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
 *
 *        computing blocks of NB columns at a time
 *
diff --git a/SRC/slatrd.f b/SRC/slatrd.f
index 9672401a..f73fecc7 100644
--- a/SRC/slatrd.f
+++ b/SRC/slatrd.f
@@ -18,7 +18,7 @@
 *
 *  SLATRD reduces NB rows and columns of a real symmetric matrix A to
 *  symmetric tridiagonal form by an orthogonal similarity
-*  transformation Q' * A * Q, and returns the matrices V and W which are
+*  transformation Q**T * A * Q, and returns the matrices V and W which are
 *  needed to apply the transformation to the unreduced part of A.
 *
 *  If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
@@ -95,7 +95,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
@@ -108,7 +108,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -117,7 +117,7 @@
 *  The elements of the vectors v together form the n-by-nb matrix V
 *  which is needed, with W, to apply the transformation to the unreduced
 *  part of the matrix, using a symmetric rank-2k update of the form:
-*  A := A - V*W' - W*V'.
+*  A := A - V*W**T - W*V**T.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with n = 5 and nb = 2:
diff --git a/SRC/slatrz.f b/SRC/slatrz.f
index 0359a267..a5852bcf 100644
--- a/SRC/slatrz.f
+++ b/SRC/slatrz.f
@@ -64,7 +64,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/slatzm.f b/SRC/slatzm.f
index 54574f32..1694dd65 100644
--- a/SRC/slatzm.f
+++ b/SRC/slatzm.f
@@ -21,8 +21,8 @@
 *
 *  SLATZM applies a Householder matrix generated by STZRQF to a matrix.
 *
-*  Let P = I - tau*u*u',   u = ( 1 ),
-*                              ( v )
+*  Let P = I - tau*u*u**T,   u = ( 1 ),
+*                                ( v )
 *  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
 *  SIDE = 'R'.
 *
@@ -110,13 +110,13 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        w := C1 + v' * C2
+*        w :=  (C1 + v**T * C2)**T
 *
          CALL SCOPY( N, C1, LDC, WORK, 1 )
          CALL SGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
+*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
 *        [ C2 ]    [ C2 ]        [ v ]
 *
          CALL SAXPY( N, -TAU, WORK, 1, C1, LDC )
@@ -130,7 +130,7 @@
          CALL SGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
+*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
 *
          CALL SAXPY( M, -TAU, WORK, 1, C1, 1 )
          CALL SGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
diff --git a/SRC/slauu2.f b/SRC/slauu2.f
index 25e9c82d..e1eb9c61 100644
--- a/SRC/slauu2.f
+++ b/SRC/slauu2.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  SLAUU2 computes the product U * U' or L' * L, where the triangular
+*  SLAUU2 computes the product U * U**T or L**T * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) REAL array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**T;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**T * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -100,7 +100,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product U * U'.
+*        Compute the product U * U**T.
 *
          DO 10 I = 1, N
             AII = A( I, I )
@@ -115,7 +115,7 @@
 *
       ELSE
 *
-*        Compute the product L' * L.
+*        Compute the product L**T * L.
 *
          DO 20 I = 1, N
             AII = A( I, I )
diff --git a/SRC/slauum.f b/SRC/slauum.f
index 581767d8..de0081ce 100644
--- a/SRC/slauum.f
+++ b/SRC/slauum.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  SLAUUM computes the product U * U' or L' * L, where the triangular
+*  SLAUUM computes the product U * U**T or L**T * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) REAL array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**T;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**T * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -112,7 +112,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the product U * U'.
+*           Compute the product U * U**T.
 *
             DO 10 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
@@ -131,7 +131,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute the product L' * L.
+*           Compute the product L**T * L.
 *
             DO 20 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
diff --git a/SRC/sorglq.f b/SRC/sorglq.f
index d284670d..8285f32d 100644
--- a/SRC/sorglq.f
+++ b/SRC/sorglq.f
@@ -185,7 +185,7 @@
                CALL SLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
      $                      LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i+ib:m,i:n) from the right
+*              Apply H**T to A(i+ib:m,i:n) from the right
 *
                CALL SLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise',
      $                      M-I-IB+1, N-I+1, IB, A( I, I ), LDA, WORK,
@@ -193,7 +193,7 @@
      $                      LDWORK )
             END IF
 *
-*           Apply H' to columns i:n of current block
+*           Apply H**T to columns i:n of current block
 *
             CALL SORGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
      $                   IINFO )
diff --git a/SRC/sorgrq.f b/SRC/sorgrq.f
index 75777395..82814d2d 100644
--- a/SRC/sorgrq.f
+++ b/SRC/sorgrq.f
@@ -193,14 +193,14 @@
                CALL SLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
      $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
+*              Apply H**T to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
 *
                CALL SLARFB( 'Right', 'Transpose', 'Backward', 'Rowwise',
      $                      II-1, N-K+I+IB-1, IB, A( II, 1 ), LDA, WORK,
      $                      LDWORK, A, LDA, WORK( IB+1 ), LDWORK )
             END IF
 *
-*           Apply H' to columns 1:n-k+i+ib-1 of current block
+*           Apply H**T to columns 1:n-k+i+ib-1 of current block
 *
             CALL SORGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
      $                   WORK, IINFO )
diff --git a/SRC/sorm2l.f b/SRC/sorm2l.f
index a261a782..e8fc91fd 100644
--- a/SRC/sorm2l.f
+++ b/SRC/sorm2l.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T * C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/sorm2r.f b/SRC/sorm2r.f
index fb907dd3..971e5397 100644
--- a/SRC/sorm2r.f
+++ b/SRC/sorm2r.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/sorml2.f b/SRC/sorml2.f
index 78f5d762..45015055 100644
--- a/SRC/sorml2.f
+++ b/SRC/sorml2.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/sormlq.f b/SRC/sormlq.f
index 54142f90..d2918767 100644
--- a/SRC/sormlq.f
+++ b/SRC/sormlq.f
@@ -242,19 +242,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL SLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
diff --git a/SRC/sormql.f b/SRC/sormql.f
index 37a2bac2..7ed15d74 100644
--- a/SRC/sormql.f
+++ b/SRC/sormql.f
@@ -239,17 +239,17 @@
      $                   A( 1, I ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL SLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
      $                   IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/sormqr.f b/SRC/sormqr.f
index 1193cf10..a35c71d6 100644
--- a/SRC/sormqr.f
+++ b/SRC/sormqr.f
@@ -235,19 +235,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL SLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
      $                   IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
diff --git a/SRC/sormr2.f b/SRC/sormr2.f
index 966f76ab..05e32932 100644
--- a/SRC/sormr2.f
+++ b/SRC/sormr2.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'T', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'T',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,8 +39,8 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m by n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
diff --git a/SRC/sormr3.f b/SRC/sormr3.f
index 9bc3430a..541a2d2b 100644
--- a/SRC/sormr3.f
+++ b/SRC/sormr3.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'T', or
+*        Q**T* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'T',
+*        C * Q**T if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a real orthogonal matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**T from the Left
+*          = 'R': apply Q or Q**T from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'T': apply Q' (Transpose)
+*          = 'T': apply Q**T (Transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -80,7 +80,7 @@
 *
 *  C       (input/output) REAL array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -181,19 +181,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**T is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**T is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**T
 *
          CALL SLARZ( SIDE, MI, NI, L, A( I, JA ), LDA, TAU( I ),
      $               C( IC, JC ), LDC, WORK )
diff --git a/SRC/sormrq.f b/SRC/sormrq.f
index 042de568..cfb72670 100644
--- a/SRC/sormrq.f
+++ b/SRC/sormrq.f
@@ -245,17 +245,17 @@
      $                   A( I, 1 ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**T is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**T is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL SLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/sormrz.f b/SRC/sormrz.f
index 149eb6c2..801f137c 100644
--- a/SRC/sormrz.f
+++ b/SRC/sormrz.f
@@ -263,19 +263,19 @@
 *
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**T is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**T is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**T
 *
             CALL SLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
diff --git a/SRC/spbcon.f b/SRC/spbcon.f
index 76a98295..0fb53dd9 100644
--- a/SRC/spbcon.f
+++ b/SRC/spbcon.f
@@ -139,7 +139,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL SLATBS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEL, WORK( 2*N+1 ),
@@ -160,7 +160,7 @@
      $                   INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL SLATBS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
      $                   KD, AB, LDAB, WORK, SCALEU, WORK( 2*N+1 ),
diff --git a/SRC/spbsv.f b/SRC/spbsv.f
index a2abc6fb..b32d58a3 100644
--- a/SRC/spbsv.f
+++ b/SRC/spbsv.f
@@ -135,7 +135,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL SPBTRF( UPLO, N, KD, AB, LDAB, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/spbsvx.f b/SRC/spbsvx.f
index 4c4d5f34..95dc5ac6 100644
--- a/SRC/spbsvx.f
+++ b/SRC/spbsvx.f
@@ -352,7 +352,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T *U or A = L*L**T.
 *
          IF( UPPER ) THEN
             DO 40 J = 1, N
diff --git a/SRC/spbtf2.f b/SRC/spbtf2.f
index f20207af..6dd688e6 100644
--- a/SRC/spbtf2.f
+++ b/SRC/spbtf2.f
@@ -20,9 +20,9 @@
 *  positive definite band matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
-*  where U is an upper triangular matrix, U' is the transpose of U, and
+*     A = U**T * U ,  if UPLO = 'U', or
+*     A = L  * L**T,  if UPLO = 'L',
+*  where U is an upper triangular matrix, U**T is the transpose of U, and
 *  L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -52,7 +52,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T*U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
@@ -137,7 +137,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T*U.
 *
          DO 10 J = 1, N
 *
@@ -161,7 +161,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/spbtrs.f b/SRC/spbtrs.f
index 00733dac..a52834b7 100644
--- a/SRC/spbtrs.f
+++ b/SRC/spbtrs.f
@@ -107,11 +107,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T *U.
 *
          DO 10 J = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**T *X = B, overwriting B with X.
 *
             CALL STBSV( 'Upper', 'Transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
@@ -123,7 +123,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**T.
 *
          DO 20 J = 1, NRHS
 *
@@ -132,7 +132,7 @@
             CALL STBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
 *
-*           Solve L'*X = B, overwriting B with X.
+*           Solve L**T *X = B, overwriting B with X.
 *
             CALL STBSV( 'Lower', 'Transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
diff --git a/SRC/spocon.f b/SRC/spocon.f
index 2880cd73..0a50fa18 100644
--- a/SRC/spocon.f
+++ b/SRC/spocon.f
@@ -129,7 +129,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL SLATRS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
@@ -147,7 +147,7 @@
      $                   A, LDA, WORK, SCALEL, WORK( 2*N+1 ), INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL SLATRS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N, A,
      $                   LDA, WORK, SCALEU, WORK( 2*N+1 ), INFO )
diff --git a/SRC/sposv.f b/SRC/sposv.f
index f88006ef..19909a35 100644
--- a/SRC/sposv.f
+++ b/SRC/sposv.f
@@ -105,7 +105,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL SPOTRF( UPLO, N, A, LDA, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/sposvx.f b/SRC/sposvx.f
index fa1c1166..090ae300 100644
--- a/SRC/sposvx.f
+++ b/SRC/sposvx.f
@@ -320,7 +320,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T *U or A = L*L**T.
 *
          CALL SLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL SPOTRF( UPLO, N, AF, LDAF, INFO )
diff --git a/SRC/spotf2.f b/SRC/spotf2.f
index fd8d1899..2b8d5157 100644
--- a/SRC/spotf2.f
+++ b/SRC/spotf2.f
@@ -20,8 +20,8 @@
 *  positive definite matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
+*     A = U**T * U ,  if UPLO = 'U', or
+*     A = L  * L**T,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -48,7 +48,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U'*U  or A = L*L'.
+*          factorization A = U**T *U  or A = L*L**T.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T *U.
 *
          DO 10 J = 1, N
 *
@@ -131,7 +131,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/spotrf.f b/SRC/spotrf.f
index 0af0c91a..45dc72be 100644
--- a/SRC/spotrf.f
+++ b/SRC/spotrf.f
@@ -116,7 +116,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the Cholesky factorization A = U'*U.
+*           Compute the Cholesky factorization A = U**T*U.
 *
             DO 10 J = 1, N, NB
 *
@@ -144,7 +144,7 @@
 *
          ELSE
 *
-*           Compute the Cholesky factorization A = L*L'.
+*           Compute the Cholesky factorization A = L*L**T.
 *
             DO 20 J = 1, N, NB
 *
diff --git a/SRC/spotri.f b/SRC/spotri.f
index 59c21cc5..401a7921 100644
--- a/SRC/spotri.f
+++ b/SRC/spotri.f
@@ -86,7 +86,7 @@
       IF( INFO.GT.0 )
      $   RETURN
 *
-*     Form inv(U)*inv(U)' or inv(L)'*inv(L).
+*     Form inv(U) * inv(U)**T or inv(L)**T * inv(L).
 *
       CALL SLAUUM( UPLO, N, A, LDA, INFO )
 *
diff --git a/SRC/spotrs.f b/SRC/spotrs.f
index 6c2c7cbb..1792841c 100644
--- a/SRC/spotrs.f
+++ b/SRC/spotrs.f
@@ -100,9 +100,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T *U.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B, overwriting B with X.
 *
          CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
@@ -113,14 +113,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**T.
 *
 *        Solve L*X = B, overwriting B with X.
 *
          CALL STRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
      $               NRHS, ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, overwriting B with X.
 *
          CALL STRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', N, NRHS,
      $               ONE, A, LDA, B, LDB )
diff --git a/SRC/sppcon.f b/SRC/sppcon.f
index ddc9ec9c..1d492754 100644
--- a/SRC/sppcon.f
+++ b/SRC/sppcon.f
@@ -128,7 +128,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**T).
 *
             CALL SLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
      $                   AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
@@ -146,7 +146,7 @@
      $                   AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**T).
 *
             CALL SLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
      $                   AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
diff --git a/SRC/sppsv.f b/SRC/sppsv.f
index 2b71a068..e0f4259e 100644
--- a/SRC/sppsv.f
+++ b/SRC/sppsv.f
@@ -117,7 +117,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**T*U or A = L*L**T.
 *
       CALL SPPTRF( UPLO, N, AP, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/sppsvx.f b/SRC/sppsvx.f
index 578785b4..b7be9041 100644
--- a/SRC/sppsvx.f
+++ b/SRC/sppsvx.f
@@ -112,17 +112,18 @@
 *                            (N*(N+1)/2)
 *          If FACT = 'F', then AFP is an input argument and on entry
 *          contains the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L', in the same storage
+*          factorization A = U**T*U or A = L*L**T, in the same storage
 *          format as A.  If EQUED .ne. 'N', then AFP is the factored
 *          form of the equilibrated matrix A.
 *
 *          If FACT = 'N', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L' of the original matrix A.
+*          factorization A = U**T * U or A = L * L**T of the original
+*          matrix A.
 *
 *          If FACT = 'E', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U'*U or A = L*L' of the equilibrated
+*          factorization A = U**T * U or A = L * L**T of the equilibrated
 *          matrix A (see the description of AP for the form of the
 *          equilibrated matrix).
 *
@@ -324,7 +325,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**T * U or A = L * L**T.
 *
          CALL SCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL SPPTRF( UPLO, N, AFP, INFO )
diff --git a/SRC/spptrf.f b/SRC/spptrf.f
index 1ec242ff..b0d7cd20 100644
--- a/SRC/spptrf.f
+++ b/SRC/spptrf.f
@@ -115,7 +115,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**T*U.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -139,7 +139,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**T.
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/spptri.f b/SRC/spptri.f
index ff4e8507..5bb7961a 100644
--- a/SRC/spptri.f
+++ b/SRC/spptri.f
@@ -95,7 +95,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product inv(U) * inv(U)'.
+*        Compute the product inv(U) * inv(U)**T.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -109,7 +109,7 @@
 *
       ELSE
 *
-*        Compute the product inv(L)' * inv(L).
+*        Compute the product inv(L)**T * inv(L).
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/spptrs.f b/SRC/spptrs.f
index d729ed13..b099f55a 100644
--- a/SRC/spptrs.f
+++ b/SRC/spptrs.f
@@ -96,11 +96,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**T * U.
 *
          DO 10 I = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**T *X = B, overwriting B with X.
 *
             CALL STPSV( 'Upper', 'Transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
@@ -112,7 +112,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L * L**T.
 *
          DO 20 I = 1, NRHS
 *
@@ -121,7 +121,7 @@
             CALL STPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
 *
-*           Solve L'*X = Y, overwriting B with X.
+*           Solve L**T *X = Y, overwriting B with X.
 *
             CALL STPSV( 'Lower', 'Transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
diff --git a/SRC/sptcon.f b/SRC/sptcon.f
index b556e8db..72666776 100644
--- a/SRC/sptcon.f
+++ b/SRC/sptcon.f
@@ -117,7 +117,7 @@
 *        m(i,j) =  abs(A(i,j)), i = j,
 *        m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**T.
 *
 *     Solve M(L) * x = e.
 *
@@ -126,7 +126,7 @@
          WORK( I ) = ONE + WORK( I-1 )*ABS( E( I-1 ) )
    20 CONTINUE
 *
-*     Solve D * M(L)' * x = b.
+*     Solve D * M(L)**T * x = b.
 *
       WORK( N ) = WORK( N ) / D( N )
       DO 30 I = N - 1, 1, -1
diff --git a/SRC/sptrfs.f b/SRC/sptrfs.f
index 865205cd..2b7e3b68 100644
--- a/SRC/sptrfs.f
+++ b/SRC/sptrfs.f
@@ -263,7 +263,7 @@
 *           m(i,j) =  abs(A(i,j)), i = j,
 *           m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**T.
 *
 *        Solve M(L) * x = e.
 *
@@ -272,7 +272,7 @@
             WORK( I ) = ONE + WORK( I-1 )*ABS( EF( I-1 ) )
    60    CONTINUE
 *
-*        Solve D * M(L)' * x = b.
+*        Solve D * M(L)**T * x = b.
 *
          WORK( N ) = WORK( N ) / DF( N )
          DO 70 I = N - 1, 1, -1
diff --git a/SRC/sptsv.f b/SRC/sptsv.f
index f46a9b25..09b08613 100644
--- a/SRC/sptsv.f
+++ b/SRC/sptsv.f
@@ -84,7 +84,7 @@
          RETURN
       END IF
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
       CALL SPTTRF( N, D, E, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/sptsvx.f b/SRC/sptsvx.f
index 4ceb9239..8e1fa861 100644
--- a/SRC/sptsvx.f
+++ b/SRC/sptsvx.f
@@ -188,7 +188,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the L*D*L' (or U'*D*U) factorization of A.
+*        Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
          CALL SCOPY( N, D, 1, DF, 1 )
          IF( N.GT.1 )
diff --git a/SRC/spttrf.f b/SRC/spttrf.f
index 1cc6a927..ab88d09c 100644
--- a/SRC/spttrf.f
+++ b/SRC/spttrf.f
@@ -15,9 +15,9 @@
 *  Purpose
 *  =======
 *
-*  SPTTRF computes the L*D*L' factorization of a real symmetric
+*  SPTTRF computes the L*D*L**T factorization of a real symmetric
 *  positive definite tridiagonal matrix A.  The factorization may also
-*  be regarded as having the form A = U'*D*U.
+*  be regarded as having the form A = U**T*D*U.
 *
 *  Arguments
 *  =========
@@ -28,14 +28,14 @@
 *  D       (input/output) REAL array, dimension (N)
 *          On entry, the n diagonal elements of the tridiagonal matrix
 *          A.  On exit, the n diagonal elements of the diagonal matrix
-*          D from the L*D*L' factorization of A.
+*          D from the L*D*L**T factorization of A.
 *
 *  E       (input/output) REAL array, dimension (N-1)
 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
 *          matrix A.  On exit, the (n-1) subdiagonal elements of the
-*          unit bidiagonal factor L from the L*D*L' factorization of A.
+*          unit bidiagonal factor L from the L*D*L**T factorization of A.
 *          E can also be regarded as the superdiagonal of the unit
-*          bidiagonal factor U from the U'*D*U factorization of A.
+*          bidiagonal factor U from the U**T*D*U factorization of A.
 *
 *  INFO    (output) INTEGER
 *          = 0: successful exit
@@ -77,7 +77,7 @@
       IF( N.EQ.0 )
      $   RETURN
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**T (or U**T*D*U) factorization of A.
 *
       I4 = MOD( N-1, 4 )
       DO 10 I = 1, I4
diff --git a/SRC/spttrs.f b/SRC/spttrs.f
index 35216666..d4a9e5f5 100644
--- a/SRC/spttrs.f
+++ b/SRC/spttrs.f
@@ -17,7 +17,7 @@
 *
 *  SPTTRS solves a tridiagonal system of the form
 *     A * X = B
-*  using the L*D*L' factorization of A computed by SPTTRF.  D is a
+*  using the L*D*L**T factorization of A computed by SPTTRF.  D is a
 *  diagonal matrix specified in the vector D, L is a unit bidiagonal
 *  matrix whose subdiagonal is specified in the vector E, and X and B
 *  are N by NRHS matrices.
@@ -34,13 +34,13 @@
 *
 *  D       (input) REAL array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          L*D*L' factorization of A.
+*          L*D*L**T factorization of A.
 *
 *  E       (input) REAL array, dimension (N-1)
 *          The (n-1) subdiagonal elements of the unit bidiagonal factor
-*          L from the L*D*L' factorization of A.  E can also be regarded
+*          L from the L*D*L**T factorization of A.  E can also be regarded
 *          as the superdiagonal of the unit bidiagonal factor U from the
-*          factorization A = U'*D*U.
+*          factorization A = U**T*D*U.
 *
 *  B       (input/output) REAL array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
diff --git a/SRC/sptts2.f b/SRC/sptts2.f
index fdc56996..6e185fda 100644
--- a/SRC/sptts2.f
+++ b/SRC/sptts2.f
@@ -17,7 +17,7 @@
 *
 *  SPTTS2 solves a tridiagonal system of the form
 *     A * X = B
-*  using the L*D*L' factorization of A computed by SPTTRF.  D is a
+*  using the L*D*L**T factorization of A computed by SPTTRF.  D is a
 *  diagonal matrix specified in the vector D, L is a unit bidiagonal
 *  matrix whose subdiagonal is specified in the vector E, and X and B
 *  are N by NRHS matrices.
@@ -34,13 +34,13 @@
 *
 *  D       (input) REAL array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          L*D*L' factorization of A.
+*          L*D*L**T factorization of A.
 *
 *  E       (input) REAL array, dimension (N-1)
 *          The (n-1) subdiagonal elements of the unit bidiagonal factor
-*          L from the L*D*L' factorization of A.  E can also be regarded
+*          L from the L*D*L**T factorization of A.  E can also be regarded
 *          as the superdiagonal of the unit bidiagonal factor U from the
-*          factorization A = U'*D*U.
+*          factorization A = U**T*D*U.
 *
 *  B       (input/output) REAL array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
@@ -68,7 +68,7 @@
          RETURN
       END IF
 *
-*     Solve A * X = B using the factorization A = L*D*L',
+*     Solve A * X = B using the factorization A = L*D*L**T,
 *     overwriting each right hand side vector with its solution.
 *
       DO 30 J = 1, NRHS
@@ -79,7 +79,7 @@
             B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
    10    CONTINUE
 *
-*           Solve D * L' * x = b.
+*           Solve D * L**T * x = b.
 *
          B( N, J ) = B( N, J ) / D( N )
          DO 20 I = N - 1, 1, -1
diff --git a/SRC/sspcon.f b/SRC/sspcon.f
index 9afbaeaf..7b2d467b 100644
--- a/SRC/sspcon.f
+++ b/SRC/sspcon.f
@@ -145,7 +145,7 @@
       CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL SSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/sspgst.f b/SRC/sspgst.f
index b8a0ca9f..f4482258 100644
--- a/SRC/sspgst.f
+++ b/SRC/sspgst.f
@@ -102,7 +102,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**T)*A*inv(U)
 *
 *           J1 and JJ are the indices of A(1,j) and A(j,j)
 *
@@ -124,7 +124,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**T)
 *
 *           KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
 *
@@ -154,7 +154,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**T
 *
 *           K1 and KK are the indices of A(1,k) and A(k,k)
 *
@@ -179,7 +179,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**T *A*L
 *
 *           JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
 *
diff --git a/SRC/sspgv.f b/SRC/sspgv.f
index 269a53d7..27ea0076 100644
--- a/SRC/sspgv.f
+++ b/SRC/sspgv.f
@@ -159,7 +159,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -175,7 +175,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/sspgvd.f b/SRC/sspgvd.f
index 682a4852..48cb24bb 100644
--- a/SRC/sspgvd.f
+++ b/SRC/sspgvd.f
@@ -191,7 +191,6 @@
          END IF
          WORK( 1 ) = LWMIN
          IWORK( 1 ) = LIWMIN
-*
          IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
             INFO = -11
          ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
@@ -237,7 +236,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -253,7 +252,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T *y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/sspgvx.f b/SRC/sspgvx.f
index f8717c8a..26f0b71c 100644
--- a/SRC/sspgvx.f
+++ b/SRC/sspgvx.f
@@ -255,7 +255,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -271,7 +271,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/sspsv.f b/SRC/sspsv.f
index de14e872..a1994997 100644
--- a/SRC/sspsv.f
+++ b/SRC/sspsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL SSPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/sspsvx.f b/SRC/sspsvx.f
index 364a7707..f1a2f868 100644
--- a/SRC/sspsvx.f
+++ b/SRC/sspsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL SCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL SSPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/ssptrd.f b/SRC/ssptrd.f
index e4eabbf0..4599f503 100644
--- a/SRC/ssptrd.f
+++ b/SRC/ssptrd.f
@@ -73,7 +73,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
@@ -86,7 +86,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
@@ -140,7 +140,7 @@
          I1 = N*( N-1 ) / 2 + 1
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)
 *
             CALL SLARFG( I, AP( I1+I-1 ), AP( I1 ), 1, TAUI )
@@ -157,13 +157,13 @@
                CALL SSPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
      $                     1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*SDOT( I, TAU, 1, AP( I1 ), 1 )
                CALL SAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL SSPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
 *
@@ -183,7 +183,7 @@
          DO 20 I = 1, N - 1
             I1I1 = II + N - I + 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)
 *
             CALL SLARFG( N-I, AP( II+1 ), AP( II+2 ), 1, TAUI )
@@ -200,14 +200,14 @@
                CALL SSPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
      $                     ZERO, TAU( I ), 1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*SDOT( N-I, TAU( I ), 1, AP( II+1 ),
      $                 1 )
                CALL SAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**T
 *
                CALL SSPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
      $                     AP( I1I1 ) )
diff --git a/SRC/ssptrf.f b/SRC/ssptrf.f
index 8e6b3bef..3b38eb83 100644
--- a/SRC/ssptrf.f
+++ b/SRC/ssptrf.f
@@ -71,7 +71,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -88,7 +88,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -153,7 +153,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -274,7 +274,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = ONE / AP( KC+K-1 )
                CALL SSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -293,8 +293,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -340,7 +340,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -468,7 +468,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = ONE / AP( KC )
                   CALL SSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -491,8 +491,11 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
+*
+*                 where L(k) and L(k+1) are the k-th and (k+1)-th
+*                 columns of L
 *
                   D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
                   D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
diff --git a/SRC/ssptri.f b/SRC/ssptri.f
index a00872bd..634f6f25 100644
--- a/SRC/ssptri.f
+++ b/SRC/ssptri.f
@@ -127,7 +127,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -228,7 +228,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/ssptrs.f b/SRC/ssptrs.f
index 80e2e716..04b95d2f 100644
--- a/SRC/ssptrs.f
+++ b/SRC/ssptrs.f
@@ -103,7 +103,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -177,7 +177,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL SGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -212,7 +212,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL SGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -234,7 +234,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -311,7 +311,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -330,7 +330,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -347,7 +347,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/ssycon.f b/SRC/ssycon.f
index 377aa804..fe5dc16a 100644
--- a/SRC/ssycon.f
+++ b/SRC/ssycon.f
@@ -148,7 +148,7 @@
       CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL SSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/ssygs2.f b/SRC/ssygs2.f
index 50c73ab8..b1b940ed 100644
--- a/SRC/ssygs2.f
+++ b/SRC/ssygs2.f
@@ -20,19 +20,19 @@
 *  to standard form.
 *
 *  If ITYPE = 1, the problem is A*x = lambda*B*x,
-*  and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
+*  and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
 *
 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-*  B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
+*  B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
 *
-*  B must have been previously factorized as U'*U or L*L' by SPOTRF.
+*  B must have been previously factorized as U**T *U or L*L**T by SPOTRF.
 *
 *  Arguments
 *  =========
 *
 *  ITYPE   (input) INTEGER
-*          = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
-*          = 2 or 3: compute U*A*U' or L'*A*L.
+*          = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
+*          = 2 or 3: compute U*A*U**T or L**T *A*L.
 *
 *  UPLO    (input) CHARACTER*1
 *          Specifies whether the upper or lower triangular part of the
@@ -115,7 +115,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**T)*A*inv(U)
 *
             DO 10 K = 1, N
 *
@@ -140,7 +140,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**T)
 *
             DO 20 K = 1, N
 *
@@ -165,7 +165,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**T
 *
             DO 30 K = 1, N
 *
@@ -185,7 +185,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**T *A*L
 *
             DO 40 K = 1, N
 *
diff --git a/SRC/ssygst.f b/SRC/ssygst.f
index e9fb56d5..7537b7b3 100644
--- a/SRC/ssygst.f
+++ b/SRC/ssygst.f
@@ -133,7 +133,7 @@
          IF( ITYPE.EQ.1 ) THEN
             IF( UPPER ) THEN
 *
-*              Compute inv(U')*A*inv(U)
+*              Compute inv(U**T)*A*inv(U)
 *
                DO 10 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -163,7 +163,7 @@
    10          CONTINUE
             ELSE
 *
-*              Compute inv(L)*A*inv(L')
+*              Compute inv(L)*A*inv(L**T)
 *
                DO 20 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -195,7 +195,7 @@
          ELSE
             IF( UPPER ) THEN
 *
-*              Compute U*A*U'
+*              Compute U*A*U**T
 *
                DO 30 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -219,7 +219,7 @@
    30          CONTINUE
             ELSE
 *
-*              Compute L'*A*L
+*              Compute L**T*A*L
 *
                DO 40 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
diff --git a/SRC/ssygv.f b/SRC/ssygv.f
index e1c623e3..a05dd701 100644
--- a/SRC/ssygv.f
+++ b/SRC/ssygv.f
@@ -195,7 +195,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -209,7 +209,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/ssygvd.f b/SRC/ssygvd.f
index 432eb1a4..6dd57381 100644
--- a/SRC/ssygvd.f
+++ b/SRC/ssygvd.f
@@ -246,7 +246,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -260,7 +260,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/ssygvx.f b/SRC/ssygvx.f
index d8446f2c..7a6aa961 100644
--- a/SRC/ssygvx.f
+++ b/SRC/ssygvx.f
@@ -296,7 +296,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -310,7 +310,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**T*y
 *
             IF( UPPER ) THEN
                TRANS = 'T'
diff --git a/SRC/ssysv.f b/SRC/ssysv.f
index 9743dd8a..fdaa147f 100644
--- a/SRC/ssysv.f
+++ b/SRC/ssysv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL SSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/ssysvx.f b/SRC/ssysvx.f
index 4dcc0e12..7776f414 100644
--- a/SRC/ssysvx.f
+++ b/SRC/ssysvx.f
@@ -254,7 +254,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL SLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL SSYTRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/ssytd2.f b/SRC/ssytd2.f
index 576450d0..e15280ee 100644
--- a/SRC/ssytd2.f
+++ b/SRC/ssytd2.f
@@ -17,7 +17,7 @@
 *  =======
 *
 *  SSYTD2 reduces a real symmetric matrix A to symmetric tridiagonal
-*  form T by an orthogonal similarity transformation: Q' * A * Q = T.
+*  form T by an orthogonal similarity transformation: Q**T * A * Q = T.
 *
 *  Arguments
 *  =========
@@ -79,7 +79,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -163,7 +163,7 @@
 *
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)
 *
             CALL SLARFG( I, A( I, I+1 ), A( 1, I+1 ), 1, TAUI )
@@ -180,13 +180,13 @@
                CALL SSYMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
      $                     TAU, 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *
                ALPHA = -HALF*TAUI*SDOT( I, TAU, 1, A( 1, I+1 ), 1 )
                CALL SAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL SSYR2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
      $                     LDA )
@@ -203,7 +203,7 @@
 *
          DO 20 I = 1, N - 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)
 *
             CALL SLARFG( N-I, A( I+1, I ), A( MIN( I+2, N ), I ), 1,
@@ -221,14 +221,14 @@
                CALL SSYMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
      $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**T * v) * v
 *
                ALPHA = -HALF*TAUI*SDOT( N-I, TAU( I ), 1, A( I+1, I ),
      $                 1 )
                CALL SAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**T
 *
                CALL SSYR2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )
diff --git a/SRC/ssytf2.f b/SRC/ssytf2.f
index c20b4747..d94f7f70 100644
--- a/SRC/ssytf2.f
+++ b/SRC/ssytf2.f
@@ -20,10 +20,10 @@
 *  SSYTF2 computes the factorization of a real symmetric matrix A using
 *  the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**T  or  A = L*D*L**T
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the transpose of U, and D is symmetric and
+*  triangular matrices, U**T is the transpose of U, and D is symmetric and
 *  block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -90,7 +90,7 @@
 *  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -107,7 +107,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -173,7 +173,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -279,7 +279,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = ONE / A( K, K )
                CALL SSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -298,8 +298,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -341,7 +341,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -450,7 +450,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   D11 = ONE / A( K, K )
                   CALL SSYR( UPLO, N-K, -D11, A( K+1, K ), 1,
@@ -468,7 +468,7 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( (A(k) A(k+1))*D(k)**(-1) ) * (A(k) A(k+1))'
+*                 A := A - ( (A(k) A(k+1))*D(k)**(-1) ) * (A(k) A(k+1))**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/ssytrd.f b/SRC/ssytrd.f
index 3399e5e3..b122d9c2 100644
--- a/SRC/ssytrd.f
+++ b/SRC/ssytrd.f
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -105,7 +105,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**T
 *
 *  where tau is a real scalar, and v is a real vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -235,7 +235,7 @@
      $                   LDWORK )
 *
 *           Update the unreduced submatrix A(1:i-1,1:i-1), using an
-*           update of the form:  A := A - V*W' - W*V'
+*           update of the form:  A := A - V*W' - W*V**T
 *
             CALL SSYR2K( UPLO, 'No transpose', I-1, NB, -ONE, A( 1, I ),
      $                   LDA, WORK, LDWORK, ONE, A, LDA )
@@ -266,7 +266,7 @@
      $                   TAU( I ), WORK, LDWORK )
 *
 *           Update the unreduced submatrix A(i+ib:n,i+ib:n), using
-*           an update of the form:  A := A - V*W' - W*V'
+*           an update of the form:  A := A - V*W' - W*V**T
 *
             CALL SSYR2K( UPLO, 'No transpose', N-I-NB+1, NB, -ONE,
      $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
diff --git a/SRC/ssytrf.f b/SRC/ssytrf.f
index 46a1af8c..6fb06d7e 100644
--- a/SRC/ssytrf.f
+++ b/SRC/ssytrf.f
@@ -87,7 +87,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -187,7 +187,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by SLASYF;
@@ -228,7 +228,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by SLASYF;
diff --git a/SRC/ssytri.f b/SRC/ssytri.f
index 0ce0701d..118fc6b2 100644
--- a/SRC/ssytri.f
+++ b/SRC/ssytri.f
@@ -127,7 +127,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -216,7 +216,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/ssytri2x.f b/SRC/ssytri2x.f
index 9c163053..ea07f029 100644
--- a/SRC/ssytri2x.f
+++ b/SRC/ssytri2x.f
@@ -153,7 +153,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
         CALL STRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -181,9 +181,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -308,7 +308,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -330,7 +330,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
          CALL STRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -358,9 +358,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -494,7 +494,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/ssytrs.f b/SRC/ssytrs.f
index 9d2c8066..80600ea2 100644
--- a/SRC/ssytrs.f
+++ b/SRC/ssytrs.f
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -178,7 +178,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL SGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -211,7 +211,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL SGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -232,7 +232,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -306,7 +306,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -323,7 +323,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -340,7 +340,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/ssytrs2.f b/SRC/ssytrs2.f
index ff212ea1..2091ac94 100644
--- a/SRC/ssytrs2.f
+++ b/SRC/ssytrs2.f
@@ -1,13 +1,12 @@
       SUBROUTINE SSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 
      $                    WORK, INFO )
 *
-*  -- LAPACK PROTOTYPE routine (version 3.2.2) --
-*
-*  -- Written by Julie Langou of the Univ. of TN    --
-*     May 2010
-*
+*  -- LAPACK PROTOTYPE routine (version 3.3.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+*     November 2010
+*
+*  -- Written by Julie Langou of the Univ. of TN    --
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -117,7 +116,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *       P' * B  
         K=N
@@ -139,11 +138,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL STRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -167,11 +166,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**T \ B) -> B   [ U**T \ (D \ (U \P**T * B) ) ]
 *
          CALL STRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**T \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -194,7 +193,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *       P' * B  
         K=1
@@ -216,11 +215,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL STRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -242,11 +241,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**T \ B) -> B   [ L**T \ (D \ (L \P**T * B) ) ]
 * 
         CALL STRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**T \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/stbrfs.f b/SRC/stbrfs.f
index 178d3afe..98a4fc9f 100644
--- a/SRC/stbrfs.f
+++ b/SRC/stbrfs.f
@@ -348,7 +348,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL STBSV( UPLO, TRANST, DIAG, N, KD, AB, LDAB,
      $                     WORK( N+1 ), 1 )
diff --git a/SRC/stgex2.f b/SRC/stgex2.f
index d77670a9..2c3ea65e 100644
--- a/SRC/stgex2.f
+++ b/SRC/stgex2.f
@@ -29,8 +29,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
+*         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
 *
 *
 *  Arguments
@@ -259,7 +259,7 @@
          IF( WANDS ) THEN
 *
 *           Strong stability test:
-*             F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A,B)))
+*           F-norm((A-QL**T*S*QR, B-QL**T*T*QR)) <= O(EPS*F-norm((A, B)))
 *
             CALL SLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
      $                   M )
@@ -334,8 +334,8 @@
 *
 *        Compute orthogonal matrix QL:
 *
-*                    QL' * LI = [ TL ]
-*                               [ 0  ]
+*                    QL**T * LI = [ TL ]
+*                                 [ 0  ]
 *        where
 *                    LI =  [      -L              ]
 *                          [ SCALE * identity(N2) ]
@@ -353,7 +353,7 @@
 *
 *        Compute orthogonal matrix RQ:
 *
-*                    IR * RQ' =   [ 0  TR],
+*                    IR * RQ**T =   [ 0  TR],
 *
 *         where IR = [ SCALE * identity(N1), R ]
 *
@@ -448,7 +448,7 @@
          IF( WANDS ) THEN
 *
 *           Strong stability test:
-*              F-norm((A-QL*S*QR', B-QL*T*QR')) <= O(EPS*F-norm((A,B)))
+*              F-norm((A-QL*S*QR**T, B-QL*T*QR**T)) <= O(EPS*F-norm((A,B)))
 *
             CALL SLACPY( 'Full', M, M, A( J1, J1 ), LDA, WORK( M*M+1 ),
      $                   M )
diff --git a/SRC/stgexc.f b/SRC/stgexc.f
index 7ff8bd6b..8c9c834d 100644
--- a/SRC/stgexc.f
+++ b/SRC/stgexc.f
@@ -33,8 +33,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**T = Q(out) * A(out) * Z(out)**T
+*         Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T
 *
 *
 *  Arguments
diff --git a/SRC/stgsen.f b/SRC/stgsen.f
index fd9702da..356e986f 100644
--- a/SRC/stgsen.f
+++ b/SRC/stgsen.f
@@ -28,7 +28,7 @@
 *
 *  STGSEN reorders the generalized real Schur decomposition of a real
 *  matrix pair (A, B) (in terms of an orthonormal equivalence trans-
-*  formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues
+*  formation Q**T * (A, B) * Z), so that a selected cluster of eigenvalues
 *  appears in the leading diagonal blocks of the upper quasi-triangular
 *  matrix A and the upper triangular B. The leading columns of Q and
 *  Z form orthonormal bases of the corresponding left and right eigen-
@@ -207,7 +207,7 @@
 *  In other words, the selected eigenvalues are the eigenvalues of
 *  (A11, B11) in:
 *
-*                U'*(A, B)*W = (A11 A12) (B11 B12) n1
+*              U**T*(A, B)*W = (A11 A12) (B11 B12) n1
 *                              ( 0  A22),( 0  B22) n2
 *                                n1  n2    n1  n2
 *
@@ -216,10 +216,10 @@
 *  (deflating subspaces) of (A, B).
 *
 *  If (A, B) has been obtained from the generalized real Schur
-*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the
+*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z**T, then the
 *  reordered generalized real Schur form of (C, D) is given by
 *
-*           (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',
+*           (C, D) = (Q*U)*(U**T*(A, B)*W)*(Z*W)**T,
 *
 *  and the first n1 columns of Q*U and Z*W span the corresponding
 *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).
@@ -241,10 +241,10 @@
 *  where sigma-min(Zu) is the smallest singular value of the
 *  (2*n1*n2)-by-(2*n1*n2) matrix
 *
-*       Zu = [ kron(In2, A11)  -kron(A22', In1) ]
-*            [ kron(In2, B11)  -kron(B22', In1) ].
+*       Zu = [ kron(In2, A11)  -kron(A22**T, In1) ]
+*            [ kron(In2, B11)  -kron(B22**T, In1) ].
 *
-*  Here, Inx is the identity matrix of size nx and A22' is the
+*  Here, Inx is the identity matrix of size nx and A22**T is the
 *  transpose of A22. kron(X, Y) is the Kronecker product between
 *  the matrices X and Y.
 *
diff --git a/SRC/stgsja.f b/SRC/stgsja.f
index d96bad59..af472d86 100644
--- a/SRC/stgsja.f
+++ b/SRC/stgsja.f
@@ -48,10 +48,10 @@
 *
 *  On exit,
 *
-*              U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R ),
+*         U**T *A*Q = D1*( 0 R ),    V**T *B*Q = D2*( 0 R ),
 *
-*  where U, V and Q are orthogonal matrices, Z' denotes the transpose
-*  of Z, R is a nonsingular upper triangular matrix, and D1 and D2 are
+*  where U, V and Q are orthogonal matrices.
+*  R is a nonsingular upper triangular matrix, and D1 and D2 are
 *  ``diagonal'' matrices, which are of the following structures:
 *
 *  If M-K-L >= 0,
@@ -247,7 +247,7 @@
 *  min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
 *  matrix B13 to the form:
 *
-*           U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
+*           U1**T *A13*Q1 = C1*R1; V1**T *B13*Q1 = S1*R1,
 *
 *  where U1, V1 and Q1 are orthogonal matrix, and Z' is the transpose
 *  of Z.  C1 and S1 are diagonal matrices satisfying
@@ -367,13 +367,13 @@
                CALL SLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
      $                      CSV, SNV, CSQ, SNQ )
 *
-*              Update (K+I)-th and (K+J)-th rows of matrix A: U'*A
+*              Update (K+I)-th and (K+J)-th rows of matrix A: U**T *A
 *
                IF( K+J.LE.M )
      $            CALL SROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
      $                       LDA, CSU, SNU )
 *
-*              Update I-th and J-th rows of matrix B: V'*B
+*              Update I-th and J-th rows of matrix B: V**T *B
 *
                CALL SROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
      $                    CSV, SNV )
diff --git a/SRC/stgsna.f b/SRC/stgsna.f
index 39fb8eea..d3db5416 100644
--- a/SRC/stgsna.f
+++ b/SRC/stgsna.f
@@ -24,7 +24,7 @@
 *  STGSNA estimates reciprocal condition numbers for specified
 *  eigenvalues and/or eigenvectors of a matrix pair (A, B) in
 *  generalized real Schur canonical form (or of any matrix pair
-*  (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where
+*  (Q*A*Z**T, Q*B*Z**T) with orthogonal matrices Q and Z, where
 *  Z' denotes the transpose of Z.
 *
 *  (A, B) must be in generalized real Schur form (as returned by SGGES),
@@ -150,12 +150,12 @@
 *  The reciprocal of the condition number of a generalized eigenvalue
 *  w = (a, b) is defined as
 *
-*       S(w) = (|u'Av|**2 + |u'Bv|**2)**(1/2) / (norm(u)*norm(v))
+*       S(w) = (|u**TAv|**2 + |u**TBv|**2)**(1/2) / (norm(u)*norm(v))
 *
 *  where u and v are the left and right eigenvectors of (A, B)
 *  corresponding to w; |z| denotes the absolute value of the complex
 *  number, and norm(u) denotes the 2-norm of the vector u.
-*  The pair (a, b) corresponds to an eigenvalue w = a/b (= u'Av/u'Bv)
+*  The pair (a, b) corresponds to an eigenvalue w = a/b (= u**TAv/u**TBv)
 *  of the matrix pair (A, B). If both a and b equal zero, then (A B) is
 *  singular and S(I) = -1 is returned.
 *
@@ -175,7 +175,7 @@
 *
 *     Suppose U and V are orthogonal transformations such that
 *
-*                U'*(A, B)*V  = (S, T) = ( a   *  ) ( b  *  )  1
+*              U**T*(A, B)*V  = (S, T) = ( a   *  ) ( b  *  )  1
 *                                        ( 0  S22 ),( 0 T22 )  n-1
 *                                          1  n-1     1 n-1
 *
@@ -201,7 +201,7 @@
 *
 *     Suppose U and V are orthogonal transformations such that
 *
-*                U'*(A, B)*V = (S, T) = ( S11  *   ) ( T11  *  )  2
+*              U**T*(A, B)*V = (S, T) = ( S11  *   ) ( T11  *  )  2
 *                                       ( 0    S22 ),( 0    T22) n-2
 *                                         2    n-2     2    n-2
 *
@@ -209,7 +209,7 @@
 *     pair (w, conjg(w)). There exist unitary matrices U1 and V1 such
 *     that
 *
-*         U1'*S11*V1 = ( s11 s12 )   and U1'*T11*V1 = ( t11 t12 )
+*       U1**T*S11*V1 = ( s11 s12 ) and U1**T*T11*V1 = ( t11 t12 )
 *                      (  0  s22 )                    (  0  t22 )
 *
 *     where the generalized eigenvalues w = s11/t11 and
@@ -226,8 +226,8 @@
 *                    [ t11  -t22 ],
 *
 *     This is done by computing (using real arithmetic) the
-*     roots of the characteristical polynomial det(Z1' * Z1 - lambda I),
-*     where Z1' denotes the conjugate transpose of Z1 and det(X) denotes
+*     roots of the characteristical polynomial det(Z1**T * Z1 - lambda I),
+*     where Z1**T denotes the transpose of Z1 and det(X) denotes
 *     the determinant of X.
 *
 *     and d2 is an upper bound on Difl((S11, T11), (S22, T22)), i.e. an
diff --git a/SRC/stgsy2.f b/SRC/stgsy2.f
index 2f57f3ce..20a4ae5e 100644
--- a/SRC/stgsy2.f
+++ b/SRC/stgsy2.f
@@ -628,7 +628,7 @@
       ELSE
 *
 *        Solve (I, J) - subsystem
-*             A(I, I)' * R(I, J) + D(I, I)' * L(J, J)  =  C(I, J)
+*             A(I, I)**T * R(I, J) + D(I, I)**T * L(J, J)  =  C(I, J)
 *             R(I, I)  * B(J, J) + L(I, J)  * E(J, J)  = -F(I, J)
 *        for I = 1, 2, ..., P, J = Q, Q - 1, ..., 1
 *
diff --git a/SRC/stgsyl.f b/SRC/stgsyl.f
index beff0470..f2c2a940 100644
--- a/SRC/stgsyl.f
+++ b/SRC/stgsyl.f
@@ -46,11 +46,11 @@
 *  Here Ik is the identity matrix of size k and X' is the transpose of
 *  X. kron(X, Y) is the Kronecker product between the matrices X and Y.
 *
-*  If TRANS = 'T', STGSYL solves the transposed system Z'*y = scale*b,
+*  If TRANS = 'T', STGSYL solves the transposed system Z**T*y = scale*b,
 *  which is equivalent to solve for R and L in
 *
-*              A' * R  + D' * L   = scale *  C           (3)
-*              R  * B' + L  * E'  = scale * (-F)
+*              A**T * R + D**T * L = scale * C           (3)
+*              R * B**T + L * E**T = scale * -F
 *
 *  This case (TRANS = 'T') is used to compute an one-norm-based estimate
 *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
@@ -485,8 +485,8 @@
       ELSE
 *
 *        Solve transposed (I, J)-subsystem
-*             A(I, I)' * R(I, J)  + D(I, I)' * L(I, J)  =  C(I, J)
-*             R(I, J)  * B(J, J)' + L(I, J)  * E(J, J)' = -F(I, J)
+*             A(I, I)**T * R(I, J)  + D(I, I)**T * L(I, J)  =  C(I, J)
+*             R(I, J)  * B(J, J)**T + L(I, J)  * E(J, J)**T = -F(I, J)
 *        for I = 1,2,..., P; J = Q, Q-1,..., 1
 *
          SCALE = ONE
diff --git a/SRC/stprfs.f b/SRC/stprfs.f
index d73f59ce..c8bd6cda 100644
--- a/SRC/stprfs.f
+++ b/SRC/stprfs.f
@@ -344,7 +344,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL STPSV( UPLO, TRANST, DIAG, N, AP, WORK( N+1 ), 1 )
                DO 220 I = 1, N
diff --git a/SRC/strevc.f b/SRC/strevc.f
index 1ffb629d..82fe2fb4 100644
--- a/SRC/strevc.f
+++ b/SRC/strevc.f
@@ -27,9 +27,9 @@
 *  The right eigenvector x and the left eigenvector y of T corresponding
 *  to an eigenvalue w are defined by:
 *  
-*     T*x = w*x,     (y**H)*T = w*(y**H)
+*     T*x = w*x,     (y**T)*T = w*(y**T)
 *  
-*  where y**H denotes the conjugate transpose of y.
+*  where y**T denotes the transpose of y.
 *  The eigenvalues are not input to this routine, but are read directly
 *  from the diagonal blocks of T.
 *  
@@ -652,7 +652,7 @@
   160          CONTINUE
 *
 *              Solve the quasi-triangular system:
-*                 (T(KI+1:N,KI+1:N) - WR)'*X = SCALE*WORK
+*                 (T(KI+1:N,KI+1:N) - WR)**T*X = SCALE*WORK
 *
                VMAX = ONE
                VCRIT = BIGNUM
@@ -689,7 +689,7 @@
      $                             SDOT( J-KI-1, T( KI+1, J ), 1,
      $                             WORK( KI+1+N ), 1 )
 *
-*                    Solve (T(J,J)-WR)'*X = WORK
+*                    Solve (T(J,J)-WR)**T*X = WORK
 *
                      CALL SLALN2( .FALSE., 1, 1, SMIN, ONE, T( J, J ),
      $                            LDT, ONE, ONE, WORK( J+N ), N, WR,
@@ -779,7 +779,7 @@
 *              Complex left eigenvector.
 *
 *               Initial solve:
-*                 ((T(KI,KI)    T(KI,KI+1) )' - (WR - I* WI))*X = 0.
+*                 ((T(KI,KI)    T(KI,KI+1) )**T - (WR - I* WI))*X = 0.
 *                 ((T(KI+1,KI) T(KI+1,KI+1))                )
 *
                IF( ABS( T( KI, KI+1 ) ).GE.ABS( T( KI+1, KI ) ) ) THEN
diff --git a/SRC/strrfs.f b/SRC/strrfs.f
index 2a368d98..42766a2b 100644
--- a/SRC/strrfs.f
+++ b/SRC/strrfs.f
@@ -338,7 +338,7 @@
          IF( KASE.NE.0 ) THEN
             IF( KASE.EQ.1 ) THEN
 *
-*              Multiply by diag(W)*inv(op(A)').
+*              Multiply by diag(W)*inv(op(A)**T).
 *
                CALL STRSV( UPLO, TRANST, DIAG, N, A, LDA, WORK( N+1 ),
      $                     1 )
diff --git a/SRC/strsen.f b/SRC/strsen.f
index 8054d6c2..724de085 100644
--- a/SRC/strsen.f
+++ b/SRC/strsen.f
@@ -158,7 +158,7 @@
 *  In other words, the selected eigenvalues are the eigenvalues of T11
 *  in:
 *
-*                Z'*T*Z = ( T11 T12 ) n1
+*          Z**T * T * Z = ( T11 T12 ) n1
 *                         (  0  T22 ) n2
 *                            n1  n2
 *
@@ -166,8 +166,8 @@
 *  of Z span the specified invariant subspace of T.
 *
 *  If T has been obtained from the real Schur factorization of a matrix
-*  A = Q*T*Q', then the reordered real Schur factorization of A is given
-*  by A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span
+*  A = Q*T*Q**T, then the reordered real Schur factorization of A is given
+*  by A = (Q*Z)*(Z**T*T*Z)*(Q*Z)**T, and the first n1 columns of Q*Z span
 *  the corresponding invariant subspace of A.
 *
 *  The reciprocal condition number of the average of the eigenvalues of
@@ -424,7 +424,7 @@
      $                      IERR )
             ELSE
 *
-*              Solve  T11'*R - R*T22' = scale*X.
+*              Solve T11**T*R - R*T22**T = scale*X.
 *
                CALL STRSYL( 'T', 'T', -1, N1, N2, T, LDT,
      $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
diff --git a/SRC/strsna.f b/SRC/strsna.f
index 5324b798..62c90af8 100644
--- a/SRC/strsna.f
+++ b/SRC/strsna.f
@@ -140,10 +140,10 @@
 *  The reciprocal of the condition number of an eigenvalue lambda is
 *  defined as
 *
-*          S(lambda) = |v'*u| / (norm(u)*norm(v))
+*          S(lambda) = |v**T*u| / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of T corresponding
-*  to lambda; v' denotes the conjugate-transpose of v, and norm(u)
+*  to lambda; v**T denotes the transpose of v, and norm(u)
 *  denotes the Euclidean norm. These reciprocal condition numbers always
 *  lie between zero (very badly conditioned) and one (very well
 *  conditioned). If n = 1, S(lambda) is defined to be 1.
@@ -403,12 +403,12 @@
 *
 *                 Form
 *
-*                 C' = WORK(2:N,2:N) + i*[rwork(1) ..... rwork(n-1) ]
-*                                        [   mu                     ]
-*                                        [         ..               ]
-*                                        [             ..           ]
-*                                        [                  mu      ]
-*                 where C' is conjugate transpose of complex matrix C,
+*                 C**T = WORK(2:N,2:N) + i*[rwork(1) ..... rwork(n-1) ]
+*                                          [   mu                     ]
+*                                          [         ..               ]
+*                                          [             ..           ]
+*                                          [                  mu      ]
+*                 where C**T is transpose of matrix C,
 *                 and RWORK is stored starting in the N+1-st column of
 *                 WORK.
 *
@@ -426,7 +426,7 @@
                   NN = 2*( N-1 )
                END IF
 *
-*              Estimate norm(inv(C'))
+*              Estimate norm(inv(C**T))
 *
                EST = ZERO
                KASE = 0
@@ -437,7 +437,7 @@
                   IF( KASE.EQ.1 ) THEN
                      IF( N2.EQ.1 ) THEN
 *
-*                       Real eigenvalue: solve C'*x = scale*c.
+*                       Real eigenvalue: solve C**T*x = scale*c.
 *
                         CALL SLAQTR( .TRUE., .TRUE., N-1, WORK( 2, 2 ),
      $                               LDWORK, DUMMY, DUMM, SCALE,
@@ -446,7 +446,7 @@
                      ELSE
 *
 *                       Complex eigenvalue: solve
-*                       C'*(p+iq) = scale*(c+id) in real arithmetic.
+*                       C**T*(p+iq) = scale*(c+id) in real arithmetic.
 *
                         CALL SLAQTR( .TRUE., .FALSE., N-1, WORK( 2, 2 ),
      $                               LDWORK, WORK( 1, N+1 ), MU, SCALE,
diff --git a/SRC/strsyl.f b/SRC/strsyl.f
index f2246acb..c947a079 100644
--- a/SRC/strsyl.f
+++ b/SRC/strsyl.f
@@ -355,17 +355,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
 *
-*        Solve    A' *X + ISGN*X*B = scale*C.
+*        Solve    A**T *X + ISGN*X*B = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-left corner column by column by
 *
-*          A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
+*          A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
 *
 *        Where
-*                   K-1                        L-1
-*          R(K,L) = SUM [A(I,K)'*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
-*                   I=1                        J=1
+*                   K-1                          L-1
+*          R(K,L) = SUM [A(I,K)**T*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]
+*                   I=1                          J=1
 *
 *        Start column loop (index = L)
 *        L1 (L2): column index of the first (last) row of X(K,L)
@@ -530,17 +530,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A'*X + ISGN*X*B' = scale*C.
+*        Solve    A**T*X + ISGN*X*B**T = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        top-right corner column by column by
 *
-*           A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L)
+*           A(K,K)**T*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
 *
 *        Where
-*                     K-1                          N
-*            R(K,L) = SUM [A(I,K)'*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)'].
-*                     I=1                        J=L+1
+*                     K-1                            N
+*            R(K,L) = SUM [A(I,K)**T*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T].
+*                     I=1                          J=L+1
 *
 *        Start column loop (index = L)
 *        L1 (L2): column index of the first (last) row of X(K,L)
@@ -714,16 +714,16 @@
 *
       ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A*X + ISGN*X*B' = scale*C.
+*        Solve    A*X + ISGN*X*B**T = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        bottom-right corner column by column by
 *
-*            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)' = C(K,L) - R(K,L)
+*            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)**T = C(K,L) - R(K,L)
 *
 *        Where
 *                      M                          N
-*            R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)'].
+*            R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)**T].
 *                    I=K+1                      J=L+1
 *
 *        Start column loop (index = L)
diff --git a/SRC/stzrqf.f b/SRC/stzrqf.f
index 9f6fef84..a7f0b777 100644
--- a/SRC/stzrqf.f
+++ b/SRC/stzrqf.f
@@ -66,9 +66,9 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
-*                                                 (   0    )
-*                                                 ( z( k ) )
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
+*                                                   (   0    )
+*                                                   ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an ( n - m ) element vector.
 *  tau and z( k ) are chosen to annihilate the elements of the kth row
@@ -149,7 +149,7 @@
      $                     LDA, A( K, M1 ), LDA, ONE, TAU, 1 )
 *
 *              Now form  a( k ) := a( k ) - tau*w
-*              and       B      := B      - tau*w*z( k )'.
+*              and       B      := B      - tau*w*z( k )**T.
 *
                CALL SAXPY( K-1, -TAU( K ), TAU, 1, A( 1, K ), 1 )
                CALL SGER( K-1, N-M, -TAU( K ), TAU, 1, A( K, M1 ), LDA,
diff --git a/SRC/stzrzf.f b/SRC/stzrzf.f
index b3f6eadd..b333b1b9 100644
--- a/SRC/stzrzf.f
+++ b/SRC/stzrzf.f
@@ -81,7 +81,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**T,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/zgbbrd.f b/SRC/zgbbrd.f
index 66e0d5c7..e5564856 100644
--- a/SRC/zgbbrd.f
+++ b/SRC/zgbbrd.f
@@ -20,20 +20,20 @@
 *  =======
 *
 *  ZGBBRD reduces a complex general m-by-n band matrix A to real upper
-*  bidiagonal form B by a unitary transformation: Q' * A * P = B.
+*  bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 *
-*  The routine computes B, and optionally forms Q or P', or computes
-*  Q'*C for a given matrix C.
+*  The routine computes B, and optionally forms Q or P**H, or computes
+*  Q**H*C for a given matrix C.
 *
 *  Arguments
 *  =========
 *
 *  VECT    (input) CHARACTER*1
-*          Specifies whether or not the matrices Q and P' are to be
+*          Specifies whether or not the matrices Q and P**H are to be
 *          formed.
-*          = 'N': do not form Q or P';
+*          = 'N': do not form Q or P**H;
 *          = 'Q': form Q only;
-*          = 'P': form P' only;
+*          = 'P': form P**H only;
 *          = 'B': form both.
 *
 *  M       (input) INTEGER
@@ -86,7 +86,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,NCC)
 *          On entry, an m-by-ncc matrix C.
-*          On exit, C is overwritten by Q'*C.
+*          On exit, C is overwritten by Q**H*C.
 *          C is not referenced if NCC = 0.
 *
 *  LDC     (input) INTEGER
@@ -165,7 +165,7 @@
          RETURN
       END IF
 *
-*     Initialize Q and P' to the unit matrix, if needed
+*     Initialize Q and P**H to the unit matrix, if needed
 *
       IF( WANTQ )
      $   CALL ZLASET( 'Full', M, M, CZERO, CONE, Q, LDQ )
@@ -338,7 +338,7 @@
 *
                IF( WANTPT ) THEN
 *
-*                 accumulate product of plane rotations in P'
+*                 accumulate product of plane rotations in P**H
 *
                   DO 60 J = J1, J2, KB1
                      CALL ZROT( N, PT( J+KUN-1, 1 ), LDPT,
diff --git a/SRC/zgbcon.f b/SRC/zgbcon.f
index 37138bb5..82d8829e 100644
--- a/SRC/zgbcon.f
+++ b/SRC/zgbcon.f
@@ -187,13 +187,13 @@
      $                   KL+KU, AB, LDAB, WORK, SCALE, RWORK, INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KL+KU, AB, LDAB, WORK, SCALE, RWORK,
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             IF( LNOTI ) THEN
                DO 30 J = N - 1, 1, -1
diff --git a/SRC/zgebd2.f b/SRC/zgebd2.f
index 5effb30f..2d2db958 100644
--- a/SRC/zgebd2.f
+++ b/SRC/zgebd2.f
@@ -17,7 +17,7 @@
 *  =======
 *
 *  ZGEBD2 reduces a complex general m by n matrix A to upper or lower
-*  real bidiagonal form B by a unitary transformation: Q' * A * P = B.
+*  real bidiagonal form B by a unitary transformation: Q**H * A * P = B.
 *
 *  If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
 *
@@ -87,7 +87,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -100,7 +100,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, v and u are complex vectors;
 *  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
@@ -170,7 +170,7 @@
             D( I ) = ALPHA
             A( I, I ) = ONE
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             IF( I.LT.N )
      $         CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
@@ -233,7 +233,7 @@
                E( I ) = ALPHA
                A( I+1, I ) = ONE
 *
-*              Apply H(i)' to A(i+1:m,i+1:n) from the left
+*              Apply H(i)**H to A(i+1:m,i+1:n) from the left
 *
                CALL ZLARF( 'Left', M-I, N-I, A( I+1, I ), 1,
      $                     DCONJG( TAUQ( I ) ), A( I+1, I+1 ), LDA,
diff --git a/SRC/zgebrd.f b/SRC/zgebrd.f
index b78bbc71..fcc4bdf2 100644
--- a/SRC/zgebrd.f
+++ b/SRC/zgebrd.f
@@ -99,7 +99,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
@@ -112,7 +112,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
@@ -232,7 +232,7 @@
      $                WORK( LDWRKX*NB+1 ), LDWRKY )
 *
 *        Update the trailing submatrix A(i+ib:m,i+ib:n), using
-*        an update of the form  A := A - V*Y' - X*U'
+*        an update of the form  A := A - V*Y**H - X*U**H
 *
          CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-I-NB+1,
      $               N-I-NB+1, NB, -ONE, A( I+NB, I ), LDA,
diff --git a/SRC/zgecon.f b/SRC/zgecon.f
index b969b58b..c74680f5 100644
--- a/SRC/zgecon.f
+++ b/SRC/zgecon.f
@@ -156,13 +156,13 @@
      $                   A, LDA, WORK, SU, RWORK( N+1 ), INFO )
          ELSE
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SU, RWORK( N+1 ),
      $                   INFO )
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Unit', NORMIN,
      $                   N, A, LDA, WORK, SL, RWORK, INFO )
diff --git a/SRC/zgehd2.f b/SRC/zgehd2.f
index 59d2fe68..b545b15a 100644
--- a/SRC/zgehd2.f
+++ b/SRC/zgehd2.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H
-*  by a unitary similarity transformation:  Q' * A * Q = H .
+*  by a unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -63,7 +63,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -134,7 +134,7 @@
          CALL ZLARF( 'Right', IHI, IHI-I, A( I+1, I ), 1, TAU( I ),
      $               A( 1, I+1 ), LDA, WORK )
 *
-*        Apply H(i)' to A(i+1:ihi,i+1:n) from the left
+*        Apply H(i)**H to A(i+1:ihi,i+1:n) from the left
 *
          CALL ZLARF( 'Left', IHI-I, N-I, A( I+1, I ), 1,
      $               DCONJG( TAU( I ) ), A( I+1, I+1 ), LDA, WORK )
diff --git a/SRC/zgehrd.f b/SRC/zgehrd.f
index 2599aad2..becbd5fe 100644
--- a/SRC/zgehrd.f
+++ b/SRC/zgehrd.f
@@ -16,7 +16,7 @@
 *  =======
 *
 *  ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by
-*  an unitary similarity transformation:  Q' * A * Q = H .
+*  an unitary similarity transformation:  Q**H * A * Q = H .
 *
 *  Arguments
 *  =========
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
@@ -223,14 +223,14 @@
             IB = MIN( NB, IHI-I )
 *
 *           Reduce columns i:i+ib-1 to Hessenberg form, returning the
-*           matrices V and T of the block reflector H = I - V*T*V'
+*           matrices V and T of the block reflector H = I - V*T*V**H
 *           which performs the reduction, and also the matrix Y = A*V*T
 *
             CALL ZLAHR2( IHI, I, IB, A( 1, I ), LDA, TAU( I ), T, LDT,
      $                   WORK, LDWORK )
 *
 *           Apply the block reflector H to A(1:ihi,i+ib:ihi) from the
-*           right, computing  A := A - Y * V'. V(i+ib,ib-1) must be set
+*           right, computing  A := A - Y * V**H. V(i+ib,ib-1) must be set
 *           to 1
 *
             EI = A( I+IB, I+IB-1 )
diff --git a/SRC/zgelq2.f b/SRC/zgelq2.f
index 57d5dec0..f0118ca4 100644
--- a/SRC/zgelq2.f
+++ b/SRC/zgelq2.f
@@ -53,11 +53,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
diff --git a/SRC/zgelqf.f b/SRC/zgelqf.f
index c4ebe462..1417b7fe 100644
--- a/SRC/zgelqf.f
+++ b/SRC/zgelqf.f
@@ -64,11 +64,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).
+*     Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
diff --git a/SRC/zgels.f b/SRC/zgels.f
index 2e52b01b..e9bb64e0 100644
--- a/SRC/zgels.f
+++ b/SRC/zgels.f
@@ -278,7 +278,7 @@
 *
 *           Least-Squares Problem min || A * X - B ||
 *
-*           B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*           B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
             CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, N, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
@@ -360,7 +360,7 @@
    30          CONTINUE
    40       CONTINUE
 *
-*           B(1:N,1:NRHS) := Q(1:N,:)' * B(1:M,1:NRHS)
+*           B(1:N,1:NRHS) := Q(1:N,:)**H * B(1:M,1:NRHS)
 *
             CALL ZUNMLQ( 'Left', 'Conjugate transpose', N, NRHS, M, A,
      $                   LDA, WORK( 1 ), B, LDB, WORK( MN+1 ), LWORK-MN,
diff --git a/SRC/zgelsx.f b/SRC/zgelsx.f
index 73182e70..40653f2f 100644
--- a/SRC/zgelsx.f
+++ b/SRC/zgelsx.f
@@ -45,8 +45,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**H [ inv(T11)*Q1**H*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  Arguments
@@ -275,7 +275,7 @@
 *
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
       CALL ZUNM2R( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA,
      $             WORK( 1 ), B, LDB, WORK( 2*MN+1 ), INFO )
@@ -293,7 +293,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          DO 50 I = 1, RANK
diff --git a/SRC/zgelsy.f b/SRC/zgelsy.f
index adacdf60..929c5117 100644
--- a/SRC/zgelsy.f
+++ b/SRC/zgelsy.f
@@ -43,8 +43,8 @@
 *     A * P = Q * [ T11 0 ] * Z
 *                 [  0  0 ]
 *  The minimum-norm solution is then
-*     X = P * Z' [ inv(T11)*Q1'*B ]
-*                [        0       ]
+*     X = P * Z**H [ inv(T11)*Q1**H*B ]
+*                  [        0         ]
 *  where Q1 consists of the first RANK columns of Q.
 *
 *  This routine is basically identical to the original xGELSX except
@@ -319,7 +319,7 @@
 *     complex workspace: 2*MN.
 *     Details of Householder rotations stored in WORK(MN+1:2*MN)
 *
-*     B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS)
+*     B(1:M,1:NRHS) := Q**H * B(1:M,1:NRHS)
 *
       CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA,
      $             WORK( 1 ), B, LDB, WORK( 2*MN+1 ), LWORK-2*MN, INFO )
@@ -338,7 +338,7 @@
    30    CONTINUE
    40 CONTINUE
 *
-*     B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS)
+*     B(1:N,1:NRHS) := Y**H * B(1:N,1:NRHS)
 *
       IF( RANK.LT.N ) THEN
          CALL ZUNMRZ( 'Left', 'Conjugate transpose', N, NRHS, RANK,
diff --git a/SRC/zgeql2.f b/SRC/zgeql2.f
index 99c20d96..0287bb00 100644
--- a/SRC/zgeql2.f
+++ b/SRC/zgeql2.f
@@ -59,7 +59,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -108,7 +108,7 @@
          ALPHA = A( M-K+I, N-K+I )
          CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) )
 *
-*        Apply H(i)' to A(1:m-k+i,1:n-k+i-1) from the left
+*        Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
 *
          A( M-K+I, N-K+I ) = ONE
          CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1,
diff --git a/SRC/zgeqlf.f b/SRC/zgeqlf.f
index 8fb64426..35799726 100644
--- a/SRC/zgeqlf.f
+++ b/SRC/zgeqlf.f
@@ -71,7 +71,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
@@ -186,7 +186,7 @@
                CALL ZLARFT( 'Backward', 'Columnwise', M-K+I+IB-1, IB,
      $                      A( 1, N-K+I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
+*              Apply H**H to A(1:m-k+i+ib-1,1:n-k+i-1) from the left
 *
                CALL ZLARFB( 'Left', 'Conjugate transpose', 'Backward',
      $                      'Columnwise', M-K+I+IB-1, N-K+I-1, IB,
diff --git a/SRC/zgeqp3.f b/SRC/zgeqp3.f
index 870d2734..234b09d9 100644
--- a/SRC/zgeqp3.f
+++ b/SRC/zgeqp3.f
@@ -79,7 +79,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a real/complex scalar, and v is a real/complex vector
 *  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
diff --git a/SRC/zgeqpf.f b/SRC/zgeqpf.f
index c5808a1a..99129134 100644
--- a/SRC/zgeqpf.f
+++ b/SRC/zgeqpf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H = I - tau * v * v'
+*     H = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
diff --git a/SRC/zgeqr2.f b/SRC/zgeqr2.f
index fb397f1f..d829a2f3 100644
--- a/SRC/zgeqr2.f
+++ b/SRC/zgeqr2.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -106,7 +106,7 @@
      $                TAU( I ) )
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             ALPHA = A( I, I )
             A( I, I ) = ONE
diff --git a/SRC/zgeqr2p.f b/SRC/zgeqr2p.f
index 6ad8feba..03a755f0 100644
--- a/SRC/zgeqr2p.f
+++ b/SRC/zgeqr2p.f
@@ -57,7 +57,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -106,7 +106,7 @@
      $                TAU( I ) )
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(i:m,i+1:n) from the left
+*           Apply H(i)**H to A(i:m,i+1:n) from the left
 *
             ALPHA = A( I, I )
             A( I, I ) = ONE
diff --git a/SRC/zgeqrf.f b/SRC/zgeqrf.f
index e0a2eeb4..9312a3e6 100644
--- a/SRC/zgeqrf.f
+++ b/SRC/zgeqrf.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**H to A(i:m,i+ib:n) from the left
 *
                CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/zgeqrfp.f b/SRC/zgeqrfp.f
index a3d1d6e5..138aeb96 100644
--- a/SRC/zgeqrfp.f
+++ b/SRC/zgeqrfp.f
@@ -69,7 +69,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
@@ -171,7 +171,7 @@
                CALL ZLARFT( 'Forward', 'Columnwise', M-I+1, IB,
      $                      A( I, I ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i:m,i+ib:n) from the left
+*              Apply H**H to A(i:m,i+ib:n) from the left
 *
                CALL ZLARFB( 'Left', 'Conjugate transpose', 'Forward',
      $                      'Columnwise', M-I+1, N-I-IB+1, IB,
diff --git a/SRC/zgerq2.f b/SRC/zgerq2.f
index ab577930..92d1aca5 100644
--- a/SRC/zgerq2.f
+++ b/SRC/zgerq2.f
@@ -55,11 +55,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
+*     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
diff --git a/SRC/zgerqf.f b/SRC/zgerqf.f
index 7a86a18b..9a825b6e 100644
--- a/SRC/zgerqf.f
+++ b/SRC/zgerqf.f
@@ -67,11 +67,11 @@
 *
 *  The matrix Q is represented as a product of elementary reflectors
 *
-*     Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
+*     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
diff --git a/SRC/zgetrs.f b/SRC/zgetrs.f
index ce459b55..c9086d23 100644
--- a/SRC/zgetrs.f
+++ b/SRC/zgetrs.f
@@ -128,12 +128,12 @@
 *
 *        Solve A**T * X = B  or A**H * X = B.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**T *X = B or U**H *X = B, overwriting B with X.
 *
          CALL ZTRSM( 'Left', 'Upper', TRANS, 'Non-unit', N, NRHS, ONE,
      $               A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**T *X = B, or L**H *X = B overwriting B with X.
 *
          CALL ZTRSM( 'Left', 'Lower', TRANS, 'Unit', N, NRHS, ONE, A,
      $               LDA, B, LDB )
diff --git a/SRC/zggglm.f b/SRC/zggglm.f
index 8f3a0352..3ede5eda 100644
--- a/SRC/zggglm.f
+++ b/SRC/zggglm.f
@@ -187,9 +187,9 @@
 *
 *     Compute the GQR factorization of matrices A and B:
 *
-*            Q'*A = ( R11 ) M,    Q'*B*Z' = ( T11   T12 ) M
-*                   (  0  ) N-M             (  0    T22 ) N-M
-*                      M                     M+P-N  N-M
+*          Q**H*A = ( R11 ) M,    Q**H*B*Z**H = ( T11   T12 ) M
+*                   (  0  ) N-M                 (  0    T22 ) N-M
+*                      M                         M+P-N  N-M
 *
 *     where R11 and T22 are upper triangular, and Q and Z are
 *     unitary.
@@ -198,8 +198,8 @@
      $             WORK( M+NP+1 ), LWORK-M-NP, INFO )
       LOPT = WORK( M+NP+1 )
 *
-*     Update left-hand-side vector d = Q'*d = ( d1 ) M
-*                                             ( d2 ) N-M
+*     Update left-hand-side vector d = Q**H*d = ( d1 ) M
+*                                               ( d2 ) N-M
 *
       CALL ZUNMQR( 'Left', 'Conjugate transpose', N, 1, M, A, LDA, WORK,
      $             D, MAX( 1, N ), WORK( M+NP+1 ), LWORK-M-NP, INFO )
@@ -246,7 +246,7 @@
          CALL ZCOPY( M, D, 1, X, 1 )
       END IF
 *
-*     Backward transformation y = Z'*y
+*     Backward transformation y = Z**H *y
 *
       CALL ZUNMRQ( 'Left', 'Conjugate transpose', P, 1, NP,
      $             B( MAX( 1, N-P+1 ), 1 ), LDB, WORK( M+1 ), Y,
diff --git a/SRC/zgglse.f b/SRC/zgglse.f
index 853b0aad..2c021cce 100644
--- a/SRC/zgglse.f
+++ b/SRC/zgglse.f
@@ -26,8 +26,8 @@
 *  M-vector, and d is a given P-vector. It is assumed that
 *  P <= N <= M+P, and
 *
-*           rank(B) = P and  rank( ( A ) ) = N.
-*                                ( ( B ) )
+*           rank(B) = P and  rank( (A) ) = N.
+*                                ( (B) )
 *
 *  These conditions ensure that the LSE problem has a unique solution,
 *  which is obtained using a generalized RQ factorization of the
@@ -183,9 +183,9 @@
 *
 *     Compute the GRQ factorization of matrices B and A:
 *
-*            B*Q' = (  0  T12 ) P   Z'*A*Q' = ( R11 R12 ) N-P
-*                     N-P  P                  (  0  R22 ) M+P-N
-*                                               N-P  P
+*            B*Q**H = (  0  T12 ) P   Z**H*A*Q**H = ( R11 R12 ) N-P
+*                        N-P  P                     (  0  R22 ) M+P-N
+*                                                      N-P  P
 *
 *     where T12 and R11 are upper triangular, and Q and Z are
 *     unitary.
@@ -194,7 +194,7 @@
      $             WORK( P+MN+1 ), LWORK-P-MN, INFO )
       LOPT = WORK( P+MN+1 )
 *
-*     Update c = Z'*c = ( c1 ) N-P
+*     Update c = Z**H *c = ( c1 ) N-P
 *                       ( c2 ) M+P-N
 *
       CALL ZUNMQR( 'Left', 'Conjugate Transpose', M, 1, MN, A, LDA,
@@ -255,7 +255,7 @@
          CALL ZAXPY( NR, -CONE, D, 1, C( N-P+1 ), 1 )
       END IF
 *
-*     Backward transformation x = Q'*x
+*     Backward transformation x = Q**H*x
 *
       CALL ZUNMRQ( 'Left', 'Conjugate Transpose', N, 1, P, B, LDB,
      $             WORK( 1 ), X, N, WORK( P+MN+1 ), LWORK-P-MN, INFO )
diff --git a/SRC/zggqrf.f b/SRC/zggqrf.f
index b04615b9..a5c652f9 100644
--- a/SRC/zggqrf.f
+++ b/SRC/zggqrf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GQR factorization
 *  of A and B implicitly gives the QR factorization of inv(B)*A:
 *
-*               inv(B)*A = Z'*(inv(T)*R)
+*               inv(B)*A = Z**H * (inv(T)*R)
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
 *  conjugate transpose of matrix Z.
 *
 *  Arguments
@@ -119,7 +119,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**H
 *
 *  where taua is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -133,7 +133,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**H
 *
 *  where taub is a complex scalar, and v is a complex vector with
 *  v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
@@ -194,7 +194,7 @@
       CALL ZGEQRF( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := Q'*B.
+*     Update B := Q**H*B.
 *
       CALL ZUNMQR( 'Left', 'Conjugate Transpose', N, P, MIN( N, M ), A,
      $             LDA, TAUA, B, LDB, WORK, LWORK, INFO )
diff --git a/SRC/zggrqf.f b/SRC/zggrqf.f
index c112c5f9..29dbf098 100644
--- a/SRC/zggrqf.f
+++ b/SRC/zggrqf.f
@@ -40,9 +40,9 @@
 *  In particular, if B is square and nonsingular, the GRQ factorization
 *  of A and B implicitly gives the RQ factorization of A*inv(B):
 *
-*               A*inv(B) = (R*inv(T))*Z'
+*               A*inv(B) = (R*inv(T))*Z**H
 *
-*  where inv(B) denotes the inverse of the matrix B, and Z' denotes the
+*  where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
 *  conjugate transpose of the matrix Z.
 *
 *  Arguments
@@ -118,7 +118,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taua * v * v'
+*     H(i) = I - taua * v * v**H
 *
 *  where taua is a complex scalar, and v is a complex vector with
 *  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
@@ -132,7 +132,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - taub * v * v'
+*     H(i) = I - taub * v * v**H
 *
 *  where taub is a complex scalar, and v is a complex vector with
 *  v(1:i-1) = 0 and v(i) = 1; v(i+1:p) is stored on exit in B(i+1:p,i),
@@ -193,7 +193,7 @@
       CALL ZGERQF( M, N, A, LDA, TAUA, WORK, LWORK, INFO )
       LOPT = WORK( 1 )
 *
-*     Update B := B*Q'
+*     Update B := B*Q**H
 *
       CALL ZUNMRQ( 'Right', 'Conjugate Transpose', P, N, MIN( M, N ),
      $             A( MAX( 1, M-N+1 ), 1 ), LDA, TAUA, B, LDB, WORK,
diff --git a/SRC/zggsvd.f b/SRC/zggsvd.f
index 6727531c..c7be33f2 100644
--- a/SRC/zggsvd.f
+++ b/SRC/zggsvd.f
@@ -24,11 +24,11 @@
 *  ZGGSVD computes the generalized singular value decomposition (GSVD)
 *  of an M-by-N complex matrix A and P-by-N complex matrix B:
 *
-*        U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R )
+*        U**H*A*Q = D1*( 0 R ),    V**H*B*Q = D2*( 0 R )
 *
-*  where U, V and Q are unitary matrices, and Z' means the conjugate
-*  transpose of Z.  Let K+L = the effective numerical rank of the
-*  matrix (A',B')', then R is a (K+L)-by-(K+L) nonsingular upper
+*  where U, V and Q are unitary matrices.
+*  Let K+L = the effective numerical rank of the
+*  matrix (A**H,B**H)**H, then R is a (K+L)-by-(K+L) nonsingular upper
 *  triangular matrix, D1 and D2 are M-by-(K+L) and P-by-(K+L) "diagonal"
 *  matrices and of the following structures, respectively:
 *
@@ -85,13 +85,13 @@
 *
 *  In particular, if B is an N-by-N nonsingular matrix, then the GSVD of
 *  A and B implicitly gives the SVD of A*inv(B):
-*                       A*inv(B) = U*(D1*inv(D2))*V'.
-*  If ( A',B')' has orthnormal columns, then the GSVD of A and B is also
+*                       A*inv(B) = U*(D1*inv(D2))*V**H.
+*  If ( A**H,B**H)**H has orthnormal columns, then the GSVD of A and B is also
 *  equal to the CS decomposition of A and B. Furthermore, the GSVD can
 *  be used to derive the solution of the eigenvalue problem:
-*                       A'*A x = lambda* B'*B x.
+*                       A**H*A x = lambda* B**H*B x.
 *  In some literature, the GSVD of A and B is presented in the form
-*                   U'*A*X = ( 0 D1 ),   V'*B*X = ( 0 D2 )
+*                   U**H*A*X = ( 0 D1 ),   V**H*B*X = ( 0 D2 )
 *  where U and V are orthogonal and X is nonsingular, and D1 and D2 are
 *  ``diagonal''.  The former GSVD form can be converted to the latter
 *  form by taking the nonsingular matrix X as
@@ -127,7 +127,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in Purpose.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**H,B**H)**H.
 *
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
 *          On entry, the M-by-N matrix A.
@@ -209,7 +209,7 @@
 *  TOLA    DOUBLE PRECISION
 *  TOLB    DOUBLE PRECISION
 *          TOLA and TOLB are the thresholds to determine the effective
-*          rank of (A',B')'. Generally, they are set to
+*          rank of (A**H,B**H)**H. Generally, they are set to
 *                   TOLA = MAX(M,N)*norm(A)*MAZHEPS,
 *                   TOLB = MAX(P,N)*norm(B)*MAZHEPS.
 *          The size of TOLA and TOLB may affect the size of backward
diff --git a/SRC/zggsvp.f b/SRC/zggsvp.f
index 8db862fd..6d2373aa 100644
--- a/SRC/zggsvp.f
+++ b/SRC/zggsvp.f
@@ -24,24 +24,23 @@
 *
 *  ZGGSVP computes unitary matrices U, V and Q such that
 *
-*                   N-K-L  K    L
-*   U'*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
-*                L ( 0     0   A23 )
-*            M-K-L ( 0     0    0  )
+*                     N-K-L  K    L
+*   U**H*A*Q =     K ( 0    A12  A13 )  if M-K-L >= 0;
+*                  L ( 0     0   A23 )
+*              M-K-L ( 0     0    0  )
 *
 *                   N-K-L  K    L
 *          =     K ( 0    A12  A13 )  if M-K-L < 0;
 *              M-K ( 0     0   A23 )
 *
-*                 N-K-L  K    L
-*   V'*B*Q =   L ( 0     0   B13 )
-*            P-L ( 0     0    0  )
+*                   N-K-L  K    L
+*   V**H*B*Q =   L ( 0     0   B13 )
+*              P-L ( 0     0    0  )
 *
 *  where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
 *  upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
 *  otherwise A23 is (M-K)-by-L upper trapezoidal.  K+L = the effective
-*  numerical rank of the (M+P)-by-N matrix (A',B')'.  Z' denotes the
-*  conjugate transpose of Z.
+*  numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H. 
 *
 *  This decomposition is the preprocessing step for computing the
 *  Generalized Singular Value Decomposition (GSVD), see subroutine
@@ -101,7 +100,7 @@
 *  L       (output) INTEGER
 *          On exit, K and L specify the dimension of the subblocks
 *          described in Purpose section.
-*          K + L = effective numerical rank of (A',B')'.
+*          K + L = effective numerical rank of (A**H,B**H)**H.
 *
 *  U       (output) COMPLEX*16 array, dimension (LDU,M)
 *          If JOBU = 'U', U contains the unitary matrix U.
@@ -268,13 +267,13 @@
 *
          CALL ZGERQ2( L, N, B, LDB, TAU, WORK, INFO )
 *
-*        Update A := A*Z'
+*        Update A := A*Z**H
 *
          CALL ZUNMR2( 'Right', 'Conjugate transpose', M, N, L, B, LDB,
      $                TAU, A, LDA, WORK, INFO )
          IF( WANTQ ) THEN
 *
-*           Update Q := Q*Z'
+*           Update Q := Q*Z**H
 *
             CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N, L, B,
      $                   LDB, TAU, Q, LDQ, WORK, INFO )
@@ -296,7 +295,7 @@
 *
 *     then the following does the complete QR decomposition of A11:
 *
-*              A11 = U*(  0  T12 )*P1'
+*              A11 = U*(  0  T12 )*P1**H
 *                      (  0   0  )
 *
       DO 70 I = 1, N - L
@@ -312,7 +311,7 @@
      $      K = K + 1
    80 CONTINUE
 *
-*     Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N )
+*     Update A12 := U**H*A12, where A12 = A( 1:M, N-L+1:N )
 *
       CALL ZUNM2R( 'Left', 'Conjugate transpose', M, L, MIN( M, N-L ),
      $             A, LDA, TAU, A( 1, N-L+1 ), LDA, WORK, INFO )
@@ -354,7 +353,7 @@
 *
          IF( WANTQ ) THEN
 *
-*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1'
+*           Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1**H
 *
             CALL ZUNMR2( 'Right', 'Conjugate transpose', N, N-L, K, A,
      $                   LDA, TAU, Q, LDQ, WORK, INFO )
diff --git a/SRC/zgtcon.f b/SRC/zgtcon.f
index 1b2e1ff7..46cb8f09 100644
--- a/SRC/zgtcon.f
+++ b/SRC/zgtcon.f
@@ -152,7 +152,7 @@
      $                   WORK, N, INFO )
          ELSE
 *
-*           Multiply by inv(L')*inv(U').
+*           Multiply by inv(L**H)*inv(U**H).
 *
             CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
      $                   IPIV, WORK, N, INFO )
diff --git a/SRC/zgtsv.f b/SRC/zgtsv.f
index 92cf4153..291ea43c 100644
--- a/SRC/zgtsv.f
+++ b/SRC/zgtsv.f
@@ -22,7 +22,7 @@
 *  where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
 *  partial pivoting.
 *
-*  Note that the equation  A'*X = B  may be solved by interchanging the
+*  Note that the equation  A**H *X = B  may be solved by interchanging the
 *  order of the arguments DU and DL.
 *
 *  Arguments
diff --git a/SRC/zhecon.f b/SRC/zhecon.f
index 5b35d75d..44ed4256 100644
--- a/SRC/zhecon.f
+++ b/SRC/zhecon.f
@@ -146,7 +146,7 @@
       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
 *
          CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/zhegs2.f b/SRC/zhegs2.f
index 05e90b50..8e28624b 100644
--- a/SRC/zhegs2.f
+++ b/SRC/zhegs2.f
@@ -20,19 +20,19 @@
 *  eigenproblem to standard form.
 *
 *  If ITYPE = 1, the problem is A*x = lambda*B*x,
-*  and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')
+*  and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
 *
 *  If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-*  B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.
+*  B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
 *
-*  B must have been previously factorized as U'*U or L*L' by ZPOTRF.
+*  B must have been previously factorized as U**H *U or L*L**H by ZPOTRF.
 *
 *  Arguments
 *  =========
 *
 *  ITYPE   (input) INTEGER
-*          = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
-*          = 2 or 3: compute U*A*U' or L'*A*L.
+*          = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
+*          = 2 or 3: compute U*A*U**H or L**H *A*L.
 *
 *  UPLO    (input) CHARACTER*1
 *          Specifies whether the upper or lower triangular part of the
@@ -119,7 +119,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**H)*A*inv(U)
 *
             DO 10 K = 1, N
 *
@@ -149,7 +149,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**H)
 *
             DO 20 K = 1, N
 *
@@ -174,7 +174,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**H
 *
             DO 30 K = 1, N
 *
@@ -194,7 +194,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**H *A*L
 *
             DO 40 K = 1, N
 *
diff --git a/SRC/zhegst.f b/SRC/zhegst.f
index 74dae9af..e2ae9ba7 100644
--- a/SRC/zhegst.f
+++ b/SRC/zhegst.f
@@ -136,7 +136,7 @@
          IF( ITYPE.EQ.1 ) THEN
             IF( UPPER ) THEN
 *
-*              Compute inv(U')*A*inv(U)
+*              Compute inv(U**H)*A*inv(U)
 *
                DO 10 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -167,7 +167,7 @@
    10          CONTINUE
             ELSE
 *
-*              Compute inv(L)*A*inv(L')
+*              Compute inv(L)*A*inv(L**H)
 *
                DO 20 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -200,7 +200,7 @@
          ELSE
             IF( UPPER ) THEN
 *
-*              Compute U*A*U'
+*              Compute U*A*U**H
 *
                DO 30 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
@@ -226,7 +226,7 @@
    30          CONTINUE
             ELSE
 *
-*              Compute L'*A*L
+*              Compute L**H*A*L
 *
                DO 40 K = 1, N, NB
                   KB = MIN( N-K+1, NB )
diff --git a/SRC/zhegv.f b/SRC/zhegv.f
index 226ae26d..4593bf54 100644
--- a/SRC/zhegv.f
+++ b/SRC/zhegv.f
@@ -197,7 +197,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -211,7 +211,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhegvd.f b/SRC/zhegvd.f
index 786cbe13..4f961ef9 100644
--- a/SRC/zhegvd.f
+++ b/SRC/zhegvd.f
@@ -270,7 +270,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -284,7 +284,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhegvx.f b/SRC/zhegvx.f
index cf11803b..f002b64b 100644
--- a/SRC/zhegvx.f
+++ b/SRC/zhegvx.f
@@ -299,7 +299,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -313,7 +313,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhesv.f b/SRC/zhesv.f
index ed6a06fc..8ea5533d 100644
--- a/SRC/zhesv.f
+++ b/SRC/zhesv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
       CALL ZHETRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zhesvx.f b/SRC/zhesvx.f
index 8591af71..a2d1313a 100644
--- a/SRC/zhesvx.f
+++ b/SRC/zhesvx.f
@@ -255,7 +255,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
          CALL ZLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL ZHETRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/zhetd2.f b/SRC/zhetd2.f
index 997e6a02..464702e6 100644
--- a/SRC/zhetd2.f
+++ b/SRC/zhetd2.f
@@ -19,7 +19,7 @@
 *
 *  ZHETD2 reduces a complex Hermitian matrix A to real symmetric
 *  tridiagonal form T by a unitary similarity transformation:
-*  Q' * A * Q = T.
+*  Q**H * A * Q = T.
 *
 *  Arguments
 *  =========
@@ -81,7 +81,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -94,7 +94,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -143,7 +143,7 @@
 *     Test the input parameters
 *
       INFO = 0
-      UPPER = LSAME( UPLO, 'U' )
+      UPPER = LSAME( UPLO, 'U')
       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
          INFO = -1
       ELSE IF( N.LT.0 ) THEN
@@ -168,7 +168,7 @@
          A( N, N ) = DBLE( A( N, N ) )
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(1:i-1,i+1)
 *
             ALPHA = A( I, I+1 )
@@ -186,13 +186,13 @@
                CALL ZHEMV( UPLO, I, TAUI, A, LDA, A( 1, I+1 ), 1, ZERO,
      $                     TAU, 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**H * v) * v
 *
                ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, A( 1, I+1 ), 1 )
                CALL ZAXPY( I, ALPHA, A( 1, I+1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**H - w * v**H
 *
                CALL ZHER2( UPLO, I, -ONE, A( 1, I+1 ), 1, TAU, 1, A,
      $                     LDA )
@@ -212,7 +212,7 @@
          A( 1, 1 ) = DBLE( A( 1, 1 ) )
          DO 20 I = 1, N - 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(i+2:n,i)
 *
             ALPHA = A( I+1, I )
@@ -230,14 +230,14 @@
                CALL ZHEMV( UPLO, N-I, TAUI, A( I+1, I+1 ), LDA,
      $                     A( I+1, I ), 1, ZERO, TAU( I ), 1 )
 *
-*              Compute  w := x - 1/2 * tau * (x'*v) * v
+*              Compute  w := x - 1/2 * tau * (x**H * v) * v
 *
                ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, A( I+1, I ),
      $                 1 )
                CALL ZAXPY( N-I, ALPHA, A( I+1, I ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**H
 *
                CALL ZHER2( UPLO, N-I, -ONE, A( I+1, I ), 1, TAU( I ), 1,
      $                     A( I+1, I+1 ), LDA )
diff --git a/SRC/zhetf2.f b/SRC/zhetf2.f
index 78c5cfe5..b1980d09 100644
--- a/SRC/zhetf2.f
+++ b/SRC/zhetf2.f
@@ -20,10 +20,10 @@
 *  ZHETF2 computes the factorization of a complex Hermitian matrix A
 *  using the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**H  or  A = L*D*L**H
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the conjugate transpose of U, and D is
+*  triangular matrices, U**H is the conjugate transpose of U, and D is
 *  Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -88,7 +88,7 @@
 *    J. Lewis, Boeing Computer Services Company
 *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -105,7 +105,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -179,7 +179,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -296,7 +296,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H
 *
                R1 = ONE / DBLE( A( K, K ) )
                CALL ZHER( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -315,8 +315,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H
 *
                IF( K.GT.2 ) THEN
 *
@@ -362,7 +362,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -482,7 +482,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H
 *
                   R1 = ONE / DBLE( A( K, K ) )
                   CALL ZHER( UPLO, N-K, -R1, A( K+1, K ), 1,
@@ -500,8 +500,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/zhetrd.f b/SRC/zhetrd.f
index e2f2001f..f406b01e 100644
--- a/SRC/zhetrd.f
+++ b/SRC/zhetrd.f
@@ -92,7 +92,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
@@ -105,7 +105,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
@@ -237,7 +237,7 @@
      $                   LDWORK )
 *
 *           Update the unreduced submatrix A(1:i-1,1:i-1), using an
-*           update of the form:  A := A - V*W' - W*V'
+*           update of the form:  A := A - V*W' - W*V**H
 *
             CALL ZHER2K( UPLO, 'No transpose', I-1, NB, -CONE,
      $                   A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA )
@@ -268,7 +268,7 @@
      $                   TAU( I ), WORK, LDWORK )
 *
 *           Update the unreduced submatrix A(i+nb:n,i+nb:n), using
-*           an update of the form:  A := A - V*W' - W*V'
+*           an update of the form:  A := A - V*W' - W*V**H
 *
             CALL ZHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE,
      $                   A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
diff --git a/SRC/zhetrf.f b/SRC/zhetrf.f
index 21085b14..5d21da9b 100644
--- a/SRC/zhetrf.f
+++ b/SRC/zhetrf.f
@@ -82,7 +82,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -99,7 +99,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -182,7 +182,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by ZLAHEF;
@@ -222,7 +222,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by ZLAHEF;
diff --git a/SRC/zhetri.f b/SRC/zhetri.f
index afe26502..8e4d66ce 100644
--- a/SRC/zhetri.f
+++ b/SRC/zhetri.f
@@ -130,7 +130,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -225,7 +225,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/zhetri2x.f b/SRC/zhetri2x.f
index 71e780eb..67ee4b96 100644
--- a/SRC/zhetri2x.f
+++ b/SRC/zhetri2x.f
@@ -156,7 +156,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
 *
         CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -184,9 +184,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**H) = (inv(U))**H
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**H)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -311,7 +311,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -333,7 +333,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**H)*inv(D)*inv(U)*P'.
 *
          CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -361,9 +361,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**H) = (inv(U))**H
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**H)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -494,7 +494,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**H)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/zhetrs.f b/SRC/zhetrs.f
index 395f7867..86a53278 100644
--- a/SRC/zhetrs.f
+++ b/SRC/zhetrs.f
@@ -108,7 +108,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -180,7 +180,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -197,7 +197,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**H(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.GT.1 ) THEN
@@ -217,7 +217,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             IF( K.GT.1 ) THEN
@@ -245,7 +245,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -320,7 +320,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -337,7 +337,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**H(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N ) THEN
@@ -358,7 +358,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/zhetrs2.f b/SRC/zhetrs2.f
index d57620d1..d0259b82 100644
--- a/SRC/zhetrs2.f
+++ b/SRC/zhetrs2.f
@@ -21,9 +21,9 @@
 *  Purpose
 *  =======
 *
-*  ZHETRS2 solves a system of linear equations A*X = B with a real
-*  Hermitian matrix A using the factorization A = U*D*U**T or
-*  A = L*D*L**T computed by ZSYTRF and converted by ZSYCONV.
+*  ZHETRS2 solves a system of linear equations A*X = B with a complex
+*  Hermitian matrix A using the factorization A = U*D*U**H or
+*  A = L*D*L**H computed by ZHETRF and converted by ZSYCONV.
 *
 *  Arguments
 *  =========
@@ -118,9 +118,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
-*       P' * B  
+*       P**T * B  
         K=N
         DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN
@@ -140,11 +140,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -169,11 +169,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**H \ B) -> B   [ U**H \ (D \ (U \P**T * B) ) ]
 *
          CALL ZTRSM('L','U','C','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**H \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -196,9 +196,9 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
-*       P' * B  
+*       P**T * B  
         K=1
         DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN
@@ -218,11 +218,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -245,11 +245,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**H \ B) -> B   [ L**H \ (D \ (L \P**T * B) ) ]
 * 
         CALL ZTRSM('L','L','C','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**H \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/zhpcon.f b/SRC/zhpcon.f
index d87fd6b6..07ccf508 100644
--- a/SRC/zhpcon.f
+++ b/SRC/zhpcon.f
@@ -142,7 +142,7 @@
       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**H) or inv(U*D*U**H).
 *
          CALL ZHPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/zhpgst.f b/SRC/zhpgst.f
index 3f560ff3..8cfa2444 100644
--- a/SRC/zhpgst.f
+++ b/SRC/zhpgst.f
@@ -108,7 +108,7 @@
       IF( ITYPE.EQ.1 ) THEN
          IF( UPPER ) THEN
 *
-*           Compute inv(U')*A*inv(U)
+*           Compute inv(U**H)*A*inv(U)
 *
 *           J1 and JJ are the indices of A(1,j) and A(j,j)
 *
@@ -131,7 +131,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute inv(L)*A*inv(L')
+*           Compute inv(L)*A*inv(L**H)
 *
 *           KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
 *
@@ -161,7 +161,7 @@
       ELSE
          IF( UPPER ) THEN
 *
-*           Compute U*A*U'
+*           Compute U*A*U**H
 *
 *           K1 and KK are the indices of A(1,k) and A(k,k)
 *
@@ -186,7 +186,7 @@
    30       CONTINUE
          ELSE
 *
-*           Compute L'*A*L
+*           Compute L**H *A*L
 *
 *           JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
 *
diff --git a/SRC/zhpgv.f b/SRC/zhpgv.f
index daa50644..269fd497 100644
--- a/SRC/zhpgv.f
+++ b/SRC/zhpgv.f
@@ -160,7 +160,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -176,7 +176,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhpgvd.f b/SRC/zhpgvd.f
index bb26e8ee..94e59043 100644
--- a/SRC/zhpgvd.f
+++ b/SRC/zhpgvd.f
@@ -91,7 +91,7 @@
 *          On exit, if INFO = 0, WORK(1) returns the required LWORK.
 *
 *  LWORK   (input) INTEGER
-*          The dimension of array WORK.
+*          The dimension of the array WORK.
 *          If N <= 1,               LWORK >= 1.
 *          If JOBZ = 'N' and N > 1, LWORK >= N.
 *          If JOBZ = 'V' and N > 1, LWORK >= 2*N.
@@ -255,7 +255,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -271,7 +271,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhpgvx.f b/SRC/zhpgvx.f
index ea41c03f..0770eebb 100644
--- a/SRC/zhpgvx.f
+++ b/SRC/zhpgvx.f
@@ -256,7 +256,7 @@
          IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
 *
 *           For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-*           backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+*           backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
 *
             IF( UPPER ) THEN
                TRANS = 'N'
@@ -272,7 +272,7 @@
          ELSE IF( ITYPE.EQ.3 ) THEN
 *
 *           For B*A*x=(lambda)*x;
-*           backtransform eigenvectors: x = L*y or U'*y
+*           backtransform eigenvectors: x = L*y or U**H *y
 *
             IF( UPPER ) THEN
                TRANS = 'C'
diff --git a/SRC/zhpsv.f b/SRC/zhpsv.f
index d6ae4a2b..811bd0f8 100644
--- a/SRC/zhpsv.f
+++ b/SRC/zhpsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
       CALL ZHPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zhpsvx.f b/SRC/zhpsvx.f
index 1e464fd7..80341a2c 100644
--- a/SRC/zhpsvx.f
+++ b/SRC/zhpsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**H or A = L*D*L**H.
 *
          CALL ZCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL ZHPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/zhptrd.f b/SRC/zhptrd.f
index d59fd0d2..403bc4c4 100644
--- a/SRC/zhptrd.f
+++ b/SRC/zhptrd.f
@@ -74,7 +74,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
@@ -87,7 +87,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
@@ -147,7 +147,7 @@
          AP( I1+N-1 ) = DBLE( AP( I1+N-1 ) )
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(1:i-1,i+1)
 *
             ALPHA = AP( I1+I-1 )
@@ -165,13 +165,13 @@
                CALL ZHPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
      $                     1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**H *v) * v
 *
                ALPHA = -HALF*TAUI*ZDOTC( I, TAU, 1, AP( I1 ), 1 )
                CALL ZAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**H - w * v**H
 *
                CALL ZHPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
 *
@@ -192,7 +192,7 @@
          DO 20 I = 1, N - 1
             I1I1 = II + N - I + 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**H
 *           to annihilate A(i+2:n,i)
 *
             ALPHA = AP( II+1 )
@@ -210,14 +210,14 @@
                CALL ZHPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
      $                     ZERO, TAU( I ), 1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**H *v) * v
 *
                ALPHA = -HALF*TAUI*ZDOTC( N-I, TAU( I ), 1, AP( II+1 ),
      $                 1 )
                CALL ZAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w' - w * v**H
 *
                CALL ZHPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
      $                     AP( I1I1 ) )
diff --git a/SRC/zhptrf.f b/SRC/zhptrf.f
index 8981cb97..d3aecf0c 100644
--- a/SRC/zhptrf.f
+++ b/SRC/zhptrf.f
@@ -71,7 +71,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**H, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -88,7 +88,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**H, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -161,7 +161,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**H using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -293,7 +293,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**H = A - W(k)*1/D(k)*W(k)**H
 *
                R1 = ONE / DBLE( AP( KC+K-1 ) )
                CALL ZHPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -312,8 +312,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**H
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**H
 *
                IF( K.GT.2 ) THEN
 *
@@ -363,7 +363,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**H using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -498,7 +498,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**H = A - W(k)*(1/D(k))*W(k)**H
 *
                   R1 = ONE / DBLE( AP( KC ) )
                   CALL ZHPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -521,8 +521,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**H
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**H
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/zhptri.f b/SRC/zhptri.f
index eadcd252..738359fc 100644
--- a/SRC/zhptri.f
+++ b/SRC/zhptri.f
@@ -130,7 +130,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -233,7 +233,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**H.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/zhptrs.f b/SRC/zhptrs.f
index cad83450..f302d89a 100644
--- a/SRC/zhptrs.f
+++ b/SRC/zhptrs.f
@@ -104,7 +104,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**H.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -179,7 +179,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -197,7 +197,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**H(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.GT.1 ) THEN
@@ -218,7 +218,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**H(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             IF( K.GT.1 ) THEN
@@ -247,7 +247,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**H.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -325,7 +325,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**H *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -344,7 +344,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**H(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N ) THEN
@@ -365,7 +365,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**H(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/zla_gbamv.f b/SRC/zla_gbamv.f
index 3cd59e53..59451f55 100644
--- a/SRC/zla_gbamv.f
+++ b/SRC/zla_gbamv.f
@@ -23,10 +23,10 @@
 *  Purpose
 *  =======
 *
-*  DLA_GBAMV  performs one of the matrix-vector operations
+*  ZLA_GBAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -48,43 +48,43 @@
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  KL      (input) INTEGER
+*  KL       (input) INTEGER
 *           The number of subdiagonals within the band of A.  KL >= 0.
 *
-*  KU      (input) INTEGER
+*  KU       (input) INTEGER
 *           The number of superdiagonals within the band of A.  KU >= 0.
 *
-*  ALPHA  - DOUBLE PRECISION
+*  ALPHA    (input) DOUBLE PRECISION
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - DOUBLE PRECISION   array of DIMENSION ( LDA, n )
-*           Before entry, the leading m by n part of the array A must
+*  AB       (input) COMPLEX*16 array of DIMENSION ( LDAB, n )
+*           Before entry, the leading m by n part of the array AB must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
-*           On entry, LDA specifies the first dimension of A as declared
-*           in the calling (sub) program. LDA must be at least
+*  LDAB     (input) INTEGER
+*           On entry, LDAB specifies the first dimension of AB as declared
+*           in the calling (sub) program. LDAB must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X       (input) DOUBLE PRECISION array, dimension
+*  X        (input) COMPLEX*16 array, dimension
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -92,17 +92,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA   - DOUBLE PRECISION
+*  BETA     (input)  DOUBLE PRECISION
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y       (input/output) DOUBLE PRECISION  array, dimension
+*  Y        (input/output) DOUBLE PRECISION  array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -110,7 +110,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/zla_geamv.f b/SRC/zla_geamv.f
index b0af67a3..add41629 100644
--- a/SRC/zla_geamv.f
+++ b/SRC/zla_geamv.f
@@ -27,7 +27,7 @@
 *  ZLA_GEAMV  performs one of the matrix-vector operations
 *
 *          y := alpha*abs(A)*abs(x) + beta*abs(y),
-*     or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
+*     or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),
 *
 *  where alpha and beta are scalars, x and y are vectors and A is an
 *  m by n matrix.
@@ -44,42 +44,42 @@
 *  Arguments
 *  ==========
 *
-*  TRANS   (input) INTEGER
+*  TRANS    (input) INTEGER
 *           On entry, TRANS specifies the operation to be performed as
 *           follows:
 *
 *             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
-*             BLAS_TRANS         y := alpha*abs(A')*abs(x) + beta*abs(y)
-*             BLAS_CONJ_TRANS    y := alpha*abs(A')*abs(x) + beta*abs(y)
+*             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
+*             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)
 *
 *           Unchanged on exit.
 *
-*  M       (input) INTEGER
+*  M        (input) INTEGER
 *           On entry, M specifies the number of rows of the matrix A.
 *           M must be at least zero.
 *           Unchanged on exit.
 *
-*  N       (input) INTEGER
+*  N        (input) INTEGER
 *           On entry, N specifies the number of columns of the matrix A.
 *           N must be at least zero.
 *           Unchanged on exit.
 *
-*  ALPHA  - DOUBLE PRECISION
+*  ALPHA    (input) DOUBLE PRECISION
 *           On entry, ALPHA specifies the scalar alpha.
 *           Unchanged on exit.
 *
-*  A      - COMPLEX*16         array of DIMENSION ( LDA, n )
+*  A        (input) COMPLEX*16 array of DIMENSION ( LDA, n )
 *           Before entry, the leading m by n part of the array A must
 *           contain the matrix of coefficients.
 *           Unchanged on exit.
 *
-*  LDA     (input) INTEGER
+*  LDA      (input) INTEGER
 *           On entry, LDA specifies the first dimension of A as declared
 *           in the calling (sub) program. LDA must be at least
 *           max( 1, m ).
 *           Unchanged on exit.
 *
-*  X      - COMPLEX*16         array of DIMENSION at least
+*  X        (input) COMPLEX*16 array of DIMENSION at least
 *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
@@ -87,17 +87,17 @@
 *           vector x.
 *           Unchanged on exit.
 *
-*  INCX    (input) INTEGER
+*  INCX     (input) INTEGER
 *           On entry, INCX specifies the increment for the elements of
 *           X. INCX must not be zero.
 *           Unchanged on exit.
 *
-*  BETA   - DOUBLE PRECISION
+*  BETA     (input) DOUBLE PRECISION
 *           On entry, BETA specifies the scalar beta. When BETA is
 *           supplied as zero then Y need not be set on input.
 *           Unchanged on exit.
 *
-*  Y       (input/output) DOUBLE PRECISION  array, dimension
+*  Y        (input/output) DOUBLE PRECISION  array, dimension
 *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
 *           and at least
 *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
@@ -105,7 +105,7 @@
 *           must contain the vector y. On exit, Y is overwritten by the
 *           updated vector y.
 *
-*  INCY    (input) INTEGER
+*  INCY     (input) INTEGER
 *           On entry, INCY specifies the increment for the elements of
 *           Y. INCY must not be zero.
 *           Unchanged on exit.
diff --git a/SRC/zlabrd.f b/SRC/zlabrd.f
index b94e7da4..bd928a79 100644
--- a/SRC/zlabrd.f
+++ b/SRC/zlabrd.f
@@ -20,7 +20,7 @@
 *
 *  ZLABRD reduces the first NB rows and columns of a complex general
 *  m by n matrix A to upper or lower real bidiagonal form by a unitary
-*  transformation Q' * A * P, and returns the matrices X and Y which
+*  transformation Q**H * A * P, and returns the matrices X and Y which
 *  are needed to apply the transformation to the unreduced part of A.
 *
 *  If m >= n, A is reduced to upper bidiagonal form; if m < n, to lower
@@ -101,7 +101,7 @@
 *
 *  Each H(i) and G(i) has the form:
 *
-*     H(i) = I - tauq * v * v'  and G(i) = I - taup * u * u'
+*     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
 *
 *  where tauq and taup are complex scalars, and v and u are complex
 *  vectors.
@@ -115,9 +115,9 @@
 *  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
 *
 *  The elements of the vectors v and u together form the m-by-nb matrix
-*  V and the nb-by-n matrix U' which are needed, with X and Y, to apply
+*  V and the nb-by-n matrix U**H which are needed, with X and Y, to apply
 *  the transformation to the unreduced part of the matrix, using a block
-*  update of the form:  A := A - V*Y' - X*U'.
+*  update of the form:  A := A - V*Y**H - X*U**H.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with nb = 2:
diff --git a/SRC/zlaed7.f b/SRC/zlaed7.f
index 8dd3aa77..393ef4f5 100644
--- a/SRC/zlaed7.f
+++ b/SRC/zlaed7.f
@@ -29,9 +29,9 @@
 *  eigenvalues and optionally eigenvectors of a dense or banded
 *  Hermitian matrix that has been reduced to tridiagonal form.
 *
-*    T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
+*    T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)
 *
-*    where Z = Q'u, u is a vector of length N with ones in the
+*    where Z = Q**Hu, u is a vector of length N with ones in the
 *    CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
 *
 *     The eigenvectors of the original matrix are stored in Q, and the
diff --git a/SRC/zlaein.f b/SRC/zlaein.f
index 9c31177c..c9c4f505 100644
--- a/SRC/zlaein.f
+++ b/SRC/zlaein.f
@@ -223,7 +223,7 @@
       DO 110 ITS = 1, N
 *
 *        Solve U*x = scale*v for a right eigenvector
-*          or U'*x = scale*v for a left eigenvector,
+*          or U**H *x = scale*v for a left eigenvector,
 *        overwriting x on v.
 *
          CALL ZLATRS( 'Upper', TRANS, 'Nonunit', NORMIN, N, B, LDB, V,
diff --git a/SRC/zlags2.f b/SRC/zlags2.f
index 6727c212..39b8d58c 100644
--- a/SRC/zlags2.f
+++ b/SRC/zlags2.f
@@ -18,28 +18,26 @@
 *  ZLAGS2 computes 2-by-2 unitary matrices U, V and Q, such
 *  that if ( UPPER ) then
 *
-*            U'*A*Q = U'*( A1 A2 )*Q = ( x  0  )
-*                        ( 0  A3 )     ( x  x  )
+*            U**H *A*Q = U**H *( A1 A2 )*Q = ( x  0  )
+*                              ( 0  A3 )     ( x  x  )
 *  and
-*            V'*B*Q = V'*( B1 B2 )*Q = ( x  0  )
-*                        ( 0  B3 )     ( x  x  )
+*            V**H*B*Q = V**H *( B1 B2 )*Q = ( x  0  )
+*                             ( 0  B3 )     ( x  x  )
 *
 *  or if ( .NOT.UPPER ) then
 *
-*            U'*A*Q = U'*( A1 0  )*Q = ( x  x  )
-*                        ( A2 A3 )     ( 0  x  )
+*            U**H *A*Q = U**H *( A1 0  )*Q = ( x  x  )
+*                              ( A2 A3 )     ( 0  x  )
 *  and
-*            V'*B*Q = V'*( B1 0  )*Q = ( x  x  )
-*                        ( B2 B3 )     ( 0  x  )
+*            V**H *B*Q = V**H *( B1 0  )*Q = ( x  x  )
+*                              ( B2 B3 )     ( 0  x  )
 *  where
 *
-*    U = (     CSU      SNU ), V = (     CSV     SNV ),
-*        ( -CONJG(SNU)  CSU )      ( -CONJG(SNV) CSV )
+*    U = (   CSU    SNU ), V = (  CSV    SNV ),
+*        ( -SNU**H  CSU )      ( -SNV**H CSV )
 *
-*    Q = (     CSQ      SNQ )
-*        ( -CONJG(SNQ)  CSQ )
-*
-*  Z' denotes the conjugate transpose of Z.
+*    Q = (   CSQ    SNQ )
+*        ( -SNQ**H  CSQ )
 *
 *  The rows of the transformed A and B are parallel. Moreover, if the
 *  input 2-by-2 matrix A is not zero, then the transformed (1,1) entry
@@ -135,8 +133,8 @@
          IF( ABS( CSL ).GE.ABS( SNL ) .OR. ABS( CSR ).GE.ABS( SNR ) )
      $        THEN
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+*           and (1,2) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA11R = CSL*A1
             UA12 = CSL*A2 + D1*SNL*A3
@@ -147,7 +145,7 @@
             AUA12 = ABS( CSL )*ABS1( A2 ) + ABS( SNL )*ABS( A3 )
             AVB12 = ABS( CSR )*ABS1( B2 ) + ABS( SNR )*ABS( B3 )
 *
-*           zero (1,2) elements of U'*A and V'*B
+*           zero (1,2) elements of U**H *A and V**H *B
 *
             IF( ( ABS( UA11R )+ABS1( UA12 ) ).EQ.ZERO ) THEN
                CALL ZLARTG( -DCMPLX( VB11R ), DCONJG( VB12 ), CSQ, SNQ,
@@ -171,8 +169,8 @@
 *
          ELSE
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,2) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+*           and (2,2) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA21 = -DCONJG( D1 )*SNL*A1
             UA22 = -DCONJG( D1 )*SNL*A2 + CSL*A3
@@ -183,7 +181,7 @@
             AUA22 = ABS( SNL )*ABS1( A2 ) + ABS( CSL )*ABS( A3 )
             AVB22 = ABS( SNR )*ABS1( B2 ) + ABS( CSR )*ABS( B3 )
 *
-*           zero (2,2) elements of U'*A and V'*B, and then swap.
+*           zero (2,2) elements of U**H *A and V**H *B, and then swap.
 *
             IF( ( ABS1( UA21 )+ABS1( UA22 ) ).EQ.ZERO ) THEN
                CALL ZLARTG( -DCONJG( VB21 ), DCONJG( VB22 ), CSQ, SNQ,
@@ -236,8 +234,8 @@
          IF( ABS( CSR ).GE.ABS( SNR ) .OR. ABS( CSL ).GE.ABS( SNL ) )
      $        THEN
 *
-*           Compute the (2,1) and (2,2) elements of U'*A and V'*B,
-*           and (2,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (2,1) and (2,2) elements of U**H *A and V**H *B,
+*           and (2,1) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA21 = -D1*SNR*A1 + CSR*A2
             UA22R = CSR*A3
@@ -248,7 +246,7 @@
             AUA21 = ABS( SNR )*ABS( A1 ) + ABS( CSR )*ABS1( A2 )
             AVB21 = ABS( SNL )*ABS( B1 ) + ABS( CSL )*ABS1( B2 )
 *
-*           zero (2,1) elements of U'*A and V'*B.
+*           zero (2,1) elements of U**H *A and V**H *B.
 *
             IF( ( ABS1( UA21 )+ABS( UA22R ) ).EQ.ZERO ) THEN
                CALL ZLARTG( DCMPLX( VB22R ), VB21, CSQ, SNQ, R )
@@ -268,8 +266,8 @@
 *
          ELSE
 *
-*           Compute the (1,1) and (1,2) elements of U'*A and V'*B,
-*           and (1,1) element of |U|'*|A| and |V|'*|B|.
+*           Compute the (1,1) and (1,2) elements of U**H *A and V**H *B,
+*           and (1,1) element of |U|**H *|A| and |V|**H *|B|.
 *
             UA11 = CSR*A1 + DCONJG( D1 )*SNR*A2
             UA12 = DCONJG( D1 )*SNR*A3
@@ -280,7 +278,7 @@
             AUA11 = ABS( CSR )*ABS( A1 ) + ABS( SNR )*ABS1( A2 )
             AVB11 = ABS( CSL )*ABS( B1 ) + ABS( SNL )*ABS1( B2 )
 *
-*           zero (1,1) elements of U'*A and V'*B, and then swap.
+*           zero (1,1) elements of U**H *A and V**H *B, and then swap.
 *
             IF( ( ABS1( UA11 )+ABS1( UA12 ) ).EQ.ZERO ) THEN
                CALL ZLARTG( VB12, VB11, CSQ, SNQ, R )
diff --git a/SRC/zlagtm.f b/SRC/zlagtm.f
index 83aff56a..7d3bdd60 100644
--- a/SRC/zlagtm.f
+++ b/SRC/zlagtm.f
@@ -189,7 +189,7 @@
   120       CONTINUE
          ELSE IF( LSAME( TRANS, 'T' ) ) THEN
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**T *X
 *
             DO 140 J = 1, NRHS
                IF( N.EQ.1 ) THEN
@@ -207,7 +207,7 @@
   140       CONTINUE
          ELSE IF( LSAME( TRANS, 'C' ) ) THEN
 *
-*           Compute B := B - A'*X
+*           Compute B := B - A**H *X
 *
             DO 160 J = 1, NRHS
                IF( N.EQ.1 ) THEN
diff --git a/SRC/zlahef.f b/SRC/zlahef.f
index 860d93a6..c37a449b 100644
--- a/SRC/zlahef.f
+++ b/SRC/zlahef.f
@@ -21,15 +21,15 @@
 *  matrix A using the Bunch-Kaufman diagonal pivoting method. The
 *  partial factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I      0     )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**H U22**H )
 *
-*  A  =  ( L11  0 ) (  D   0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) (  0  A22 ) (  0    I   )
+*  A  =  ( L11  0 ) (  D   0  ) ( L11**H L21**H )  if UPLO = 'L'
+*        ( L21  I ) (  0  A22 ) (  0      I     )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
-*  Note that U' denotes the conjugate transpose of U.
+*  Note that U**H denotes the conjugate transpose of U.
 *
 *  ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code
 *  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
@@ -344,7 +344,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**H = A11 - U12*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)
@@ -593,7 +593,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**H = A22 - L21*W**H
 *
 *        computing blocks of NB columns at a time (note that conjg(W) is
 *        actually stored)
diff --git a/SRC/zlahr2.f b/SRC/zlahr2.f
index e6bffc2d..db310900 100644
--- a/SRC/zlahr2.f
+++ b/SRC/zlahr2.f
@@ -19,8 +19,8 @@
 *  ZLAHR2 reduces the first NB columns of A complex general n-BY-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by an unitary similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**H * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
 *
 *  This is an auxiliary routine called by ZGEHRD.
 *
@@ -75,7 +75,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -84,7 +84,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**H) * (A - Y*V**H).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -144,14 +144,14 @@
 *
 *           Update A(K+1:N,I)
 *
-*           Update I-th column of A - Y * V'
+*           Update I-th column of A - Y * V**H
 *
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) 
             CALL ZGEMV( 'NO TRANSPOSE', N-K, I-1, -ONE, Y(K+1,1), LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( K+1, I ), 1 )
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA ) 
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T' * V**H to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -166,13 +166,13 @@
      $                  I-1, A( K+1, 1 ),
      $                  LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**H * b2
 *
             CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, 
      $                  ONE, A( K+I, 1 ),
      $                  LDA, A( K+I, I ), 1, ONE, T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**H * w
 *
             CALL ZTRMV( 'Upper', 'Conjugate transpose', 'NON-UNIT', 
      $                  I-1, T, LDT,
diff --git a/SRC/zlahrd.f b/SRC/zlahrd.f
index 3ad16848..81d039cb 100644
--- a/SRC/zlahrd.f
+++ b/SRC/zlahrd.f
@@ -19,8 +19,8 @@
 *  ZLAHRD reduces the first NB columns of a complex general n-by-(n-k+1)
 *  matrix A so that elements below the k-th subdiagonal are zero. The
 *  reduction is performed by a unitary similarity transformation
-*  Q' * A * Q. The routine returns the matrices V and T which determine
-*  Q as a block reflector I - V*T*V', and also the matrix Y = A * V * T.
+*  Q**H * A * Q. The routine returns the matrices V and T which determine
+*  Q as a block reflector I - V*T*V**H, and also the matrix Y = A * V * T.
 *
 *  This is an OBSOLETE auxiliary routine. 
 *  This routine will be 'deprecated' in a  future release.
@@ -76,7 +76,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i+k-1) = 0, v(i+k) = 1; v(i+k+1:n) is stored on exit in
@@ -85,7 +85,7 @@
 *  The elements of the vectors v together form the (n-k+1)-by-nb matrix
 *  V which is needed, with T and Y, to apply the transformation to the
 *  unreduced part of the matrix, using an update of the form:
-*  A := (I - V*T*V') * (A - Y*V').
+*  A := (I - V*T*V**H) * (A - Y*V**H).
 *
 *  The contents of A on exit are illustrated by the following example
 *  with n = 7, k = 3 and nb = 2:
@@ -132,14 +132,14 @@
 *
 *           Update A(1:n,i)
 *
-*           Compute i-th column of A - Y * V'
+*           Compute i-th column of A - Y * V**H
 *
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )
             CALL ZGEMV( 'No transpose', N, I-1, -ONE, Y, LDY,
      $                  A( K+I-1, 1 ), LDA, ONE, A( 1, I ), 1 )
             CALL ZLACGV( I-1, A( K+I-1, 1 ), LDA )
 *
-*           Apply I - V * T' * V' to this column (call it b) from the
+*           Apply I - V * T**H * V**H to this column (call it b) from the
 *           left, using the last column of T as workspace
 *
 *           Let  V = ( V1 )   and   b = ( b1 )   (first I-1 rows)
@@ -147,19 +147,19 @@
 *
 *           where V1 is unit lower triangular
 *
-*           w := V1' * b1
+*           w := V1**H * b1
 *
             CALL ZCOPY( I-1, A( K+1, I ), 1, T( 1, NB ), 1 )
             CALL ZTRMV( 'Lower', 'Conjugate transpose', 'Unit', I-1,
      $                  A( K+1, 1 ), LDA, T( 1, NB ), 1 )
 *
-*           w := w + V2'*b2
+*           w := w + V2**H *b2
 *
             CALL ZGEMV( 'Conjugate transpose', N-K-I+1, I-1, ONE,
      $                  A( K+I, 1 ), LDA, A( K+I, I ), 1, ONE,
      $                  T( 1, NB ), 1 )
 *
-*           w := T'*w
+*           w := T**H *w
 *
             CALL ZTRMV( 'Upper', 'Conjugate transpose', 'Non-unit', I-1,
      $                  T, LDT, T( 1, NB ), 1 )
diff --git a/SRC/zlaic1.f b/SRC/zlaic1.f
index c5c8ff6d..5b73020d 100644
--- a/SRC/zlaic1.f
+++ b/SRC/zlaic1.f
@@ -41,7 +41,7 @@
 *      diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
 *                                            [ conjg(gamma) ]
 *
-*  where  alpha =  conjg(x)'*w.
+*  where  alpha =  x**H * w.
 *
 *  Arguments
 *  =========
diff --git a/SRC/zlalsd.f b/SRC/zlalsd.f
index 24594c79..24cf5515 100644
--- a/SRC/zlalsd.f
+++ b/SRC/zlalsd.f
@@ -245,7 +245,7 @@
          END IF
 *
 *        In the real version, B is passed to DLASDQ and multiplied
-*        internally by Q'. Here B is complex and that product is
+*        internally by Q**H. Here B is complex and that product is
 *        computed below in two steps (real and imaginary parts).
 *
          J = IRWB - 1
@@ -431,7 +431,7 @@
                END IF
 *
 *              In the real version, B is passed to DLASDQ and multiplied
-*              internally by Q'. Here B is complex and that product is
+*              internally by Q**H. Here B is complex and that product is
 *              computed below in two steps (real and imaginary parts).
 *
                J = IRWB - 1
diff --git a/SRC/zlaqhb.f b/SRC/zlaqhb.f
index 6526162f..4ae039f5 100644
--- a/SRC/zlaqhb.f
+++ b/SRC/zlaqhb.f
@@ -18,8 +18,8 @@
 *  Purpose
 *  =======
 *
-*  ZLAQHB equilibrates a symmetric band matrix A using the scaling
-*  factors in the vector S.
+*  ZLAQHB equilibrates a Hermitian band matrix A 
+*  using the scaling factors in the vector S.
 *
 *  Arguments
 *  =========
@@ -46,7 +46,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**H *U or A = L*L**H of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/zlaqp2.f b/SRC/zlaqp2.f
index cacdea61..0e70a495 100644
--- a/SRC/zlaqp2.f
+++ b/SRC/zlaqp2.f
@@ -136,7 +136,7 @@
 *
          IF( I.LT.N ) THEN
 *
-*           Apply H(i)' to A(offset+i:m,i+1:n) from the left.
+*           Apply H(i)**H to A(offset+i:m,i+1:n) from the left.
 *
             AII = A( OFFPI, I )
             A( OFFPI, I ) = CONE
diff --git a/SRC/zlaqps.f b/SRC/zlaqps.f
index cca63527..5dc52070 100644
--- a/SRC/zlaqps.f
+++ b/SRC/zlaqps.f
@@ -76,7 +76,7 @@
 *          Auxiliar vector.
 *
 *  F       (input/output) COMPLEX*16 array, dimension (LDF,NB)
-*          Matrix F' = L*Y'*A.
+*          Matrix F**H = L * Y**H * A.
 *
 *  LDF     (input) INTEGER
 *          The leading dimension of the array F. LDF >= max(1,N).
@@ -88,6 +88,11 @@
 *    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
 *    X. Sun, Computer Science Dept., Duke University, USA
 *
+*  Partial column norm updating strategy modified by
+*    Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
+*    University of Zagreb, Croatia.
+*     June 2010
+*  For more details see LAPACK Working Note 176.
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -141,7 +146,7 @@
          END IF
 *
 *        Apply previous Householder reflectors to column K:
-*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
+*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**H.
 *
          IF( K.GT.1 ) THEN
             DO 20 J = 1, K - 1
@@ -167,7 +172,7 @@
 *
 *        Compute Kth column of F:
 *
-*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
+*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**H*A(RK:M,K).
 *
          IF( K.LT.N ) THEN
             CALL ZGEMV( 'Conjugate transpose', M-RK+1, N-K, TAU( K ),
@@ -182,7 +187,7 @@
    40    CONTINUE
 *
 *        Incremental updating of F:
-*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
+*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**H
 *                    *A(RK:M,K).
 *
          IF( K.GT.1 ) THEN
@@ -195,7 +200,7 @@
          END IF
 *
 *        Update the current row of A:
-*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
+*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**H.
 *
          IF( K.LT.N ) THEN
             CALL ZGEMM( 'No transpose', 'Conjugate transpose', 1, N-K,
@@ -236,7 +241,7 @@
 *
 *     Apply the block reflector to the rest of the matrix:
 *     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
-*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
+*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**H.
 *
       IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
          CALL ZGEMM( 'No transpose', 'Conjugate transpose', M-RK, N-KB,
diff --git a/SRC/zlaqsb.f b/SRC/zlaqsb.f
index 666109b7..5ec4adb4 100644
--- a/SRC/zlaqsb.f
+++ b/SRC/zlaqsb.f
@@ -46,7 +46,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**T *U or A = L*L**T of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
diff --git a/SRC/zlar1v.f b/SRC/zlar1v.f
index 6183b64a..fdd8e5b5 100644
--- a/SRC/zlar1v.f
+++ b/SRC/zlar1v.f
@@ -25,14 +25,14 @@
 *
 *  ZLAR1V computes the (scaled) r-th column of the inverse of
 *  the sumbmatrix in rows B1 through BN of the tridiagonal matrix
-*  L D L^T - sigma I. When sigma is close to an eigenvalue, the
+*  L D L**T - sigma I. When sigma is close to an eigenvalue, the
 *  computed vector is an accurate eigenvector. Usually, r corresponds
 *  to the index where the eigenvector is largest in magnitude.
 *  The following steps accomplish this computation :
-*  (a) Stationary qd transform,  L D L^T - sigma I = L(+) D(+) L(+)^T,
-*  (b) Progressive qd transform, L D L^T - sigma I = U(-) D(-) U(-)^T,
+*  (a) Stationary qd transform,  L D L**T - sigma I = L(+) D(+) L(+)**T,
+*  (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T,
 *  (c) Computation of the diagonal elements of the inverse of
-*      L D L^T - sigma I by combining the above transforms, and choosing
+*      L D L**T - sigma I by combining the above transforms, and choosing
 *      r as the index where the diagonal of the inverse is (one of the)
 *      largest in magnitude.
 *  (d) Computation of the (scaled) r-th column of the inverse using the
@@ -43,18 +43,18 @@
 *  =========
 *
 *  N        (input) INTEGER
-*           The order of the matrix L D L^T.
+*           The order of the matrix L D L**T.
 *
 *  B1       (input) INTEGER
-*           First index of the submatrix of L D L^T.
+*           First index of the submatrix of L D L**T.
 *
 *  BN       (input) INTEGER
-*           Last index of the submatrix of L D L^T.
+*           Last index of the submatrix of L D L**T.
 *
 *  LAMBDA    (input) DOUBLE PRECISION
 *           The shift. In order to compute an accurate eigenvector,
 *           LAMBDA should be a good approximation to an eigenvalue
-*           of L D L^T.
+*           of L D L**T.
 *
 *  L        (input) DOUBLE PRECISION array, dimension (N-1)
 *           The (n-1) subdiagonal elements of the unit bidiagonal matrix
@@ -86,20 +86,20 @@
 *
 *  NEGCNT   (output) INTEGER
 *           If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin
-*           in the  matrix factorization L D L^T, and NEGCNT = -1 otherwise.
+*           in the  matrix factorization L D L**T, and NEGCNT = -1 otherwise.
 *
 *  ZTZ      (output) DOUBLE PRECISION
 *           The square of the 2-norm of Z.
 *
 *  MINGMA   (output) DOUBLE PRECISION
 *           The reciprocal of the largest (in magnitude) diagonal
-*           element of the inverse of L D L^T - sigma I.
+*           element of the inverse of L D L**T - sigma I.
 *
 *  R        (input/output) INTEGER
 *           The twist index for the twisted factorization used to
 *           compute Z.
 *           On input, 0 <= R <= N. If R is input as 0, R is set to
-*           the index where (L D L^T - sigma I)^{-1} is largest
+*           the index where (L D L**T - sigma I)^{-1} is largest
 *           in magnitude. If 1 <= R <= N, R is unchanged.
 *           On output, R contains the twist index used to compute Z.
 *           Ideally, R designates the position of the maximum entry in the
diff --git a/SRC/zlarf.f b/SRC/zlarf.f
index 7b05ed3c..4ff7362a 100644
--- a/SRC/zlarf.f
+++ b/SRC/zlarf.f
@@ -22,13 +22,13 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
 *  If tau = 0, then H is taken to be the unit matrix.
 *
-*  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
+*  To apply H**H, supply conjg(tau) instead
 *  tau.
 *
 *  Arguments
@@ -126,12 +126,12 @@
 *
          IF( LASTV.GT.0 ) THEN
 *
-*           w(1:lastc,1) := C(1:lastv,1:lastc)' * v(1:lastv,1)
+*           w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
 *
             CALL ZGEMV( 'Conjugate transpose', LASTV, LASTC, ONE,
      $           C, LDC, V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)'
+*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
 *
             CALL ZGERC( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
          END IF
@@ -146,7 +146,7 @@
             CALL ZGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
      $           V, INCV, ZERO, WORK, 1 )
 *
-*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)'
+*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
 *
             CALL ZGERC( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
          END IF
diff --git a/SRC/zlarfb.f b/SRC/zlarfb.f
index dbed8f57..a2b93be8 100644
--- a/SRC/zlarfb.f
+++ b/SRC/zlarfb.f
@@ -19,19 +19,19 @@
 *  Purpose
 *  =======
 *
-*  ZLARFB applies a complex block reflector H or its transpose H' to a
+*  ZLARFB applies a complex block reflector H or its transpose H**H to a
 *  complex M-by-N matrix C, from either the left or the right.
 *
 *  Arguments
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**H from the Left
+*          = 'R': apply H or H**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Conjugate transpose)
+*          = 'C': apply H**H (Conjugate transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -76,7 +76,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -157,15 +157,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
                LASTC = ILAZLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C**H * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
-*              W := C1'
+*              W := C1**H
 *
                DO 10 J = 1, K
                   CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
@@ -178,23 +178,23 @@
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2
+*                 W := W + C2**H *V2
 *
                   CALL ZGEMM( 'Conjugate transpose', 'No transpose',
      $                 LASTC, K, LASTV-K, ONE, C( K+1, 1 ), LDC,
      $                 V( K+1, 1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**H
 *
                IF( M.GT.K ) THEN
 *
-*                 C2 := C2 - V2 * W'
+*                 C2 := C2 - V2 * W**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTV-K, LASTC, K,
@@ -202,12 +202,12 @@
      $                 ONE, C( K+1, 1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**H
 *
                DO 30 J = 1, K
                   DO 20 I = 1, LASTC
@@ -217,7 +217,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
                LASTC = ILAZLR( M, LASTV, C, LDC )
@@ -244,16 +244,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - W * V2'
+*                 C2 := C2 - W * V2**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, LASTV-K, K,
@@ -261,7 +261,7 @@
      $                 ONE, C( 1, K+1 ), LDC )
                END IF
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
@@ -283,15 +283,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILAZLR( M, K, V, LDV ) )
                LASTC = ILAZLC( LASTV, N, C, LDC )
 *
-*              W := C' * V  =  (C1'*V1 + C2'*V2)  (stored in WORK)
+*              W := C' * V  =  (C1**H * V1 + C2**H * V2)  (stored in WORK)
 *
-*              W := C2'
+*              W := C2**H
 *
                DO 70 J = 1, K
                   CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -306,7 +306,7 @@
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1
+*                 W := W + C1**H*V1
 *
                   CALL ZGEMM( 'Conjugate transpose', 'No transpose',
      $                 LASTC, K, LASTV-K,
@@ -314,16 +314,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V * W'
+*              C := C - V * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1 * W'
+*                 C1 := C1 - V1 * W**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTV-K, LASTC, K,
@@ -331,13 +331,13 @@
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**H
 *
                DO 90 J = 1, K
                   DO 80 I = 1, LASTC
@@ -348,7 +348,7 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILAZLR( N, K, V, LDV ) )
                LASTC = ILAZLR( M, LASTV, C, LDC )
@@ -376,23 +376,23 @@
      $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - W * V'
+*              C := C - W * V**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - W * V1'
+*                 C1 := C1 - W * V1**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, LASTV-K, K, -ONE, WORK, LDWORK, V, LDV,
      $                 ONE, C, LDC )
                END IF
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( LASTV-K+1, 1 ), LDV,
@@ -418,28 +418,28 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
                LASTC = ILAZLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
-*              W := C1'
+*              W := C1**H
 *
                DO 130 J = 1, K
                   CALL ZCOPY( LASTC, C( J, 1 ), LDC, WORK( 1, J ), 1 )
                   CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
   130          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2'*V2'
+*                 W := W + C2**H*V2**H
 *
                   CALL ZGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTC, K, LASTV-K,
@@ -447,16 +447,16 @@
      $                 ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL ZTRMM( 'Right', 'Upper', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**H * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C2 := C2 - V2' * W'
+*                 C2 := C2 - V2**H * W**H
 *
                   CALL ZGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTV-K, LASTC, K,
@@ -469,7 +469,7 @@
                CALL ZTRMM( 'Right', 'Upper', 'No transpose', 'Unit',
      $              LASTC, K, ONE, V, LDV, WORK, LDWORK )
 *
-*              C1 := C1 - W'
+*              C1 := C1 - W**H
 *
                DO 150 J = 1, K
                   DO 140 I = 1, LASTC
@@ -479,12 +479,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
                LASTC = ILAZLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C1
 *
@@ -492,20 +492,20 @@
                   CALL ZCOPY( LASTC, C( 1, J ), 1, WORK( 1, J ), 1 )
   160          CONTINUE
 *
-*              W := W * V1'
+*              W := W * V1**H
 *
                CALL ZTRMM( 'Right', 'Upper', 'Conjugate transpose',
      $                     'Unit', LASTC, K, ONE, V, LDV, WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C2 * V2'
+*                 W := W + C2 * V2**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, K, LASTV-K, ONE, C( 1, K+1 ), LDC,
      $                 V( 1, K+1 ), LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL ZTRMM( 'Right', 'Upper', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
@@ -544,15 +544,15 @@
 *
             IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*              Form  H * C  or  H' * C  where  C = ( C1 )
-*                                                  ( C2 )
+*              Form  H * C  or  H**H * C  where  C = ( C1 )
+*                                                    ( C2 )
 *
                LASTV = MAX( K, ILAZLC( K, M, V, LDV ) )
                LASTC = ILAZLC( LASTV, N, C, LDC )
 *
-*              W := C' * V'  =  (C1'*V1' + C2'*V2') (stored in WORK)
+*              W := C**H * V**H  =  (C1**H * V1**H + C2**H * V2**H) (stored in WORK)
 *
-*              W := C2'
+*              W := C2**H
 *
                DO 190 J = 1, K
                   CALL ZCOPY( LASTC, C( LASTV-K+J, 1 ), LDC,
@@ -560,30 +560,30 @@
                   CALL ZLACGV( LASTC, WORK( 1, J ), 1 )
   190          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1'*V1'
+*                 W := W + C1**H * V1**H
 *
                   CALL ZGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTC, K, LASTV-K,
      $                 ONE, C, LDC, V, LDV, ONE, WORK, LDWORK )
                END IF
 *
-*              W := W * T'  or  W * T
+*              W := W * T**H  or  W * T
 *
                CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
 *
-*              C := C - V' * W'
+*              C := C - V**H * W**H
 *
                IF( LASTV.GT.K ) THEN
 *
-*                 C1 := C1 - V1' * W'
+*                 C1 := C1 - V1**H * W**H
 *
                   CALL ZGEMM( 'Conjugate transpose',
      $                 'Conjugate transpose', LASTV-K, LASTC, K,
@@ -596,7 +596,7 @@
      $              LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
 *
-*              C2 := C2 - W'
+*              C2 := C2 - W**H
 *
                DO 210 J = 1, K
                   DO 200 I = 1, LASTC
@@ -607,12 +607,12 @@
 *
             ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*              Form  C * H  or  C * H'  where  C = ( C1  C2 )
+*              Form  C * H  or  C * H**H  where  C = ( C1  C2 )
 *
                LASTV = MAX( K, ILAZLC( K, N, V, LDV ) )
                LASTC = ILAZLR( M, LASTV, C, LDC )
 *
-*              W := C * V'  =  (C1*V1' + C2*V2')  (stored in WORK)
+*              W := C * V**H  =  (C1*V1**H + C2*V2**H)  (stored in WORK)
 *
 *              W := C2
 *
@@ -621,21 +621,21 @@
      $                 WORK( 1, J ), 1 )
   220          CONTINUE
 *
-*              W := W * V2'
+*              W := W * V2**H
 *
                CALL ZTRMM( 'Right', 'Lower', 'Conjugate transpose',
      $              'Unit', LASTC, K, ONE, V( 1, LASTV-K+1 ), LDV,
      $              WORK, LDWORK )
                IF( LASTV.GT.K ) THEN
 *
-*                 W := W + C1 * V1'
+*                 W := W + C1 * V1**H
 *
                   CALL ZGEMM( 'No transpose', 'Conjugate transpose',
      $                 LASTC, K, LASTV-K, ONE, C, LDC, V, LDV, ONE,
      $                 WORK, LDWORK )
                END IF
 *
-*              W := W * T  or  W * T'
+*              W := W * T  or  W * T**H
 *
                CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit',
      $              LASTC, K, ONE, T, LDT, WORK, LDWORK )
diff --git a/SRC/zlarfg.f b/SRC/zlarfg.f
index 6d9742fe..1c338837 100644
--- a/SRC/zlarfg.f
+++ b/SRC/zlarfg.f
@@ -19,13 +19,13 @@
 *  ZLARFG generates a complex elementary reflector H of order n, such
 *  that
 *
-*        H' * ( alpha ) = ( beta ),   H' * H = I.
-*             (   x   )   (   0  )
+*        H**H * ( alpha ) = ( beta ),   H**H * H = I.
+*               (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, with beta real, and x is an
 *  (n-1)-element complex vector. H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**H ) ,
 *                      ( v )
 *
 *  where tau is a complex scalar and v is a complex (n-1)-element
diff --git a/SRC/zlarfgp.f b/SRC/zlarfgp.f
index 98c44a41..bc8af144 100644
--- a/SRC/zlarfgp.f
+++ b/SRC/zlarfgp.f
@@ -19,13 +19,13 @@
 *  ZLARFGP generates a complex elementary reflector H of order n, such
 *  that
 *
-*        H' * ( alpha ) = ( beta ),   H' * H = I.
-*             (   x   )   (   0  )
+*        H**H * ( alpha ) = ( beta ),   H**H * H = I.
+*               (   x   )   (   0  )
 *
 *  where alpha and beta are scalars, beta is real and non-negative, and
 *  x is an (n-1)-element complex vector.  H is represented in the form
 *
-*        H = I - tau * ( 1 ) * ( 1 v' ) ,
+*        H = I - tau * ( 1 ) * ( 1 v**H ) ,
 *                      ( v )
 *
 *  where tau is a complex scalar and v is a complex (n-1)-element
diff --git a/SRC/zlarft.f b/SRC/zlarft.f
index 954f8e24..a3e85c32 100644
--- a/SRC/zlarft.f
+++ b/SRC/zlarft.f
@@ -26,12 +26,12 @@
 *  If STOREV = 'C', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th column of the array V, and
 *
-*     H  =  I - V * T * V'
+*     H  =  I - V * T * V**H
 *
 *  If STOREV = 'R', the vector which defines the elementary reflector
 *  H(i) is stored in the i-th row of the array V, and
 *
-*     H  =  I - V' * T * V
+*     H  =  I - V**H * T * V
 *
 *  Arguments
 *  =========
@@ -150,7 +150,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)' * V(i:j,i)
+*                 T(1:i-1,i) := - tau(i) * V(i:j,1:i-1)**H * V(i:j,i)
 *
                   CALL ZGEMV( 'Conjugate transpose', J-I+1, I-1,
      $                        -TAU( I ), V( I, 1 ), LDV, V( I, I ), 1,
@@ -162,7 +162,7 @@
                   END DO
                   J = MIN( LASTV, PREVLASTV )
 *
-*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)'
+*                 T(1:i-1,i) := - tau(i) * V(1:i-1,i:j) * V(i,i:j)**H
 *
                   IF( I.LT.J )
      $               CALL ZLACGV( J-I, V( I, I+1 ), LDV )
@@ -211,7 +211,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(j:n-k+i,i+1:k)' * V(j:n-k+i,i)
+*                            - tau(i) * V(j:n-k+i,i+1:k)**H * V(j:n-k+i,i)
 *
                      CALL ZGEMV( 'Conjugate transpose', N-K+I-J+1, K-I,
      $                           -TAU( I ), V( J, I+1 ), LDV, V( J, I ),
@@ -227,7 +227,7 @@
                      J = MAX( LASTV, PREVLASTV )
 *
 *                    T(i+1:k,i) :=
-*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)'
+*                            - tau(i) * V(i+1:k,j:n-k+i) * V(i,j:n-k+i)**H
 *
                      CALL ZLACGV( N-K+I-1-J+1, V( I, J ), LDV )
                      CALL ZGEMV( 'No transpose', K-I, N-K+I-J+1,
diff --git a/SRC/zlarfx.f b/SRC/zlarfx.f
index 60354d96..686f0e20 100644
--- a/SRC/zlarfx.f
+++ b/SRC/zlarfx.f
@@ -22,7 +22,7 @@
 *  matrix C, from either the left or the right. H is represented in the
 *  form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
diff --git a/SRC/zlarrv.f b/SRC/zlarrv.f
index 854872f2..1849c76a 100644
--- a/SRC/zlarrv.f
+++ b/SRC/zlarrv.f
@@ -25,7 +25,7 @@
 *  =======
 *
 *  ZLARRV computes the eigenvectors of the tridiagonal matrix
-*  T = L D L^T given L, D and APPROXIMATIONS to the eigenvalues of L D L^T.
+*  T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
 *  The input eigenvalues should have been computed by DLARRE.
 *
 *  Arguments
diff --git a/SRC/zlarz.f b/SRC/zlarz.f
index d235191f..f2a90d04 100644
--- a/SRC/zlarz.f
+++ b/SRC/zlarz.f
@@ -21,13 +21,13 @@
 *  M-by-N matrix C, from either the left or the right. H is represented
 *  in the form
 *
-*        H = I - tau * v * v'
+*        H = I - tau * v * v**H
 *
 *  where tau is a complex scalar and v is a complex vector.
 *
 *  If tau = 0, then H is taken to be the unit matrix.
 *
-*  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
+*  To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
 *  tau.
 *
 *  H is a product of k elementary reflectors as returned by ZTZRZF.
@@ -105,7 +105,7 @@
             CALL ZCOPY( N, C, LDC, WORK, 1 )
             CALL ZLACGV( N, WORK, 1 )
 *
-*           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) )
+*           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
 *
             CALL ZGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
      $                  LDC, V, INCV, ONE, WORK, 1 )
@@ -116,7 +116,7 @@
             CALL ZAXPY( N, -TAU, WORK, 1, C, LDC )
 *
 *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                               tau * v( 1:l ) * conjg( w( 1:n )' )
+*                               tau * v( 1:l ) * w( 1:n )**H
 *
             CALL ZGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
      $                  LDC )
@@ -142,7 +142,7 @@
             CALL ZAXPY( M, -TAU, WORK, 1, C, 1 )
 *
 *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
-*                               tau * w( 1:m ) * v( 1:l )'
+*                               tau * w( 1:m ) * v( 1:l )**H
 *
             CALL ZGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
      $                  LDC )
diff --git a/SRC/zlarzb.f b/SRC/zlarzb.f
index bb51f60c..0ee12379 100644
--- a/SRC/zlarzb.f
+++ b/SRC/zlarzb.f
@@ -27,12 +27,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply H or H' from the Left
-*          = 'R': apply H or H' from the Right
+*          = 'L': apply H or H**H from the Left
+*          = 'R': apply H or H**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply H (No transpose)
-*          = 'C': apply H' (Conjugate transpose)
+*          = 'C': apply H**H (Conjugate transpose)
 *
 *  DIRECT  (input) CHARACTER*1
 *          Indicates how H is formed from a product of elementary
@@ -77,7 +77,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the M-by-N matrix C.
-*          On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
+*          On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -140,28 +140,28 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        Form  H * C  or  H' * C
+*        Form  H * C  or  H**H * C
 *
-*        W( 1:n, 1:k ) = conjg( C( 1:k, 1:n )' )
+*        W( 1:n, 1:k ) = C( 1:k, 1:n )**H
 *
          DO 10 J = 1, K
             CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
    10    CONTINUE
 *
 *        W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
-*                        conjg( C( m-l+1:m, 1:n )' ) * V( 1:k, 1:l )'
+*                        C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T
 *
          IF( L.GT.0 )
      $      CALL ZGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
      $                  ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
      $                  LDWORK )
 *
-*        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T'  or  W( 1:m, 1:k ) * T
+*        W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T  or  W( 1:m, 1:k ) * T
 *
          CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
      $               LDT, WORK, LDWORK )
 *
-*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - conjg( W( 1:n, 1:k )' )
+*        C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
 *
          DO 30 J = 1, N
             DO 20 I = 1, K
@@ -170,7 +170,7 @@
    30    CONTINUE
 *
 *        C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
-*                    conjg( V( 1:k, 1:l )' ) * conjg( W( 1:n, 1:k )' )
+*                            V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
 *
          IF( L.GT.0 )
      $      CALL ZGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
@@ -178,7 +178,7 @@
 *
       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
 *
-*        Form  C * H  or  C * H'
+*        Form  C * H  or  C * H**H
 *
 *        W( 1:m, 1:k ) = C( 1:m, 1:k )
 *
@@ -187,14 +187,14 @@
    40    CONTINUE
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
-*                        C( 1:m, n-l+1:n ) * conjg( V( 1:k, 1:l )' )
+*                        C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
 *
          IF( L.GT.0 )
      $      CALL ZGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
      $                  C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
 *
 *        W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T )  or
-*                        W( 1:m, 1:k ) * conjg( T' )
+*                        W( 1:m, 1:k ) * T**H
 *
          DO 50 J = 1, K
             CALL ZLACGV( K-J+1, T( J, J ), 1 )
diff --git a/SRC/zlarzt.f b/SRC/zlarzt.f
index e283d572..2ae745ee 100644
--- a/SRC/zlarzt.f
+++ b/SRC/zlarzt.f
@@ -164,7 +164,7 @@
 *
             IF( I.LT.K ) THEN
 *
-*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)'
+*              T(i+1:k,i) = - tau(i) * V(i+1:k,1:n) * V(i,1:n)**H
 *
                CALL ZLACGV( N, V( I, 1 ), LDV )
                CALL ZGEMV( 'No transpose', K-I, N, -TAU( I ),
diff --git a/SRC/zlasyf.f b/SRC/zlasyf.f
index 1e29fccb..a4a8d547 100644
--- a/SRC/zlasyf.f
+++ b/SRC/zlasyf.f
@@ -21,15 +21,15 @@
 *  A using the Bunch-Kaufman diagonal pivoting method. The partial
 *  factorization has the form:
 *
-*  A  =  ( I  U12 ) ( A11  0  ) (  I    0   )  if UPLO = 'U', or:
-*        ( 0  U22 ) (  0   D  ) ( U12' U22' )
+*  A  =  ( I  U12 ) ( A11  0  ) (  I       0    )  if UPLO = 'U', or:
+*        ( 0  U22 ) (  0   D  ) ( U12**T U22**T )
 *
-*  A  =  ( L11  0 ) ( D    0  ) ( L11' L21' )  if UPLO = 'L'
-*        ( L21  I ) ( 0   A22 ) (  0    I   )
+*  A  =  ( L11  0 ) ( D    0  ) ( L11**T L21**T )  if UPLO = 'L'
+*        ( L21  I ) ( 0   A22 ) (  0       I    )
 *
 *  where the order of D is at most NB. The actual order is returned in
 *  the argument KB, and is either NB or NB-1, or N if N <= NB.
-*  Note that U' denotes the transpose of U.
+*  Note that U**T denotes the transpose of U.
 *
 *  ZLASYF is an auxiliary routine called by ZSYTRF. It uses blocked code
 *  (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or
@@ -322,7 +322,7 @@
 *
 *        Update the upper triangle of A11 (= A(1:k,1:k)) as
 *
-*        A11 := A11 - U12*D*U12' = A11 - U12*W'
+*        A11 := A11 - U12*D*U12**T = A11 - U12*W**T
 *
 *        computing blocks of NB columns at a time
 *
@@ -546,7 +546,7 @@
 *
 *        Update the lower triangle of A22 (= A(k:n,k:n)) as
 *
-*        A22 := A22 - L21*D*L21' = A22 - L21*W'
+*        A22 := A22 - L21*D*L21**T = A22 - L21*W**T
 *
 *        computing blocks of NB columns at a time
 *
diff --git a/SRC/zlatrd.f b/SRC/zlatrd.f
index 73609eb2..5203189b 100644
--- a/SRC/zlatrd.f
+++ b/SRC/zlatrd.f
@@ -19,7 +19,7 @@
 *
 *  ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
 *  Hermitian tridiagonal form by a unitary similarity
-*  transformation Q' * A * Q, and returns the matrices V and W which are
+*  transformation Q**H * A * Q, and returns the matrices V and W which are
 *  needed to apply the transformation to the unreduced part of A.
 *
 *  If UPLO = 'U', ZLATRD reduces the last NB rows and columns of a
@@ -96,7 +96,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
@@ -109,7 +109,7 @@
 *
 *  Each H(i) has the form
 *
-*     H(i) = I - tau * v * v'
+*     H(i) = I - tau * v * v**H
 *
 *  where tau is a complex scalar, and v is a complex vector with
 *  v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
@@ -118,7 +118,7 @@
 *  The elements of the vectors v together form the n-by-nb matrix V
 *  which is needed, with W, to apply the transformation to the unreduced
 *  part of the matrix, using a Hermitian rank-2k update of the form:
-*  A := A - V*W' - W*V'.
+*  A := A - V*W**H - W*V**H.
 *
 *  The contents of A on exit are illustrated by the following examples
 *  with n = 5 and nb = 2:
diff --git a/SRC/zlatrz.f b/SRC/zlatrz.f
index 438522e2..ca50049c 100644
--- a/SRC/zlatrz.f
+++ b/SRC/zlatrz.f
@@ -64,7 +64,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/zlatzm.f b/SRC/zlatzm.f
index 6e5d887c..caa10780 100644
--- a/SRC/zlatzm.f
+++ b/SRC/zlatzm.f
@@ -21,8 +21,8 @@
 *
 *  ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
 *
-*  Let P = I - tau*u*u',   u = ( 1 ),
-*                              ( v )
+*  Let P = I - tau*u*u**H,   u = ( 1 ),
+*                                ( v )
 *  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
 *  SIDE = 'R'.
 *
@@ -112,14 +112,14 @@
 *
       IF( LSAME( SIDE, 'L' ) ) THEN
 *
-*        w :=  conjg( C1 + v' * C2 )
+*        w :=  ( C1 + v**H * C2 )**H
 *
          CALL ZCOPY( N, C1, LDC, WORK, 1 )
          CALL ZLACGV( N, WORK, 1 )
          CALL ZGEMV( 'Conjugate transpose', M-1, N, ONE, C2, LDC, V,
      $               INCV, ONE, WORK, 1 )
 *
-*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
+*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
 *        [ C2 ]    [ C2 ]        [ v ]
 *
          CALL ZLACGV( N, WORK, 1 )
@@ -134,7 +134,7 @@
          CALL ZGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
      $               WORK, 1 )
 *
-*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
+*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
 *
          CALL ZAXPY( M, -TAU, WORK, 1, C1, 1 )
          CALL ZGERC( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
diff --git a/SRC/zlauu2.f b/SRC/zlauu2.f
index 84010fad..b8fd4d65 100644
--- a/SRC/zlauu2.f
+++ b/SRC/zlauu2.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  ZLAUU2 computes the product U * U' or L' * L, where the triangular
+*  ZLAUU2 computes the product U * U**H or L**H * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**H;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**H * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -100,7 +100,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the product U * U'.
+*        Compute the product U * U**H.
 *
          DO 10 I = 1, N
             AII = A( I, I )
@@ -119,7 +119,7 @@
 *
       ELSE
 *
-*        Compute the product L' * L.
+*        Compute the product L**H * L.
 *
          DO 20 I = 1, N
             AII = A( I, I )
diff --git a/SRC/zlauum.f b/SRC/zlauum.f
index e2aade0e..b257d02f 100644
--- a/SRC/zlauum.f
+++ b/SRC/zlauum.f
@@ -16,7 +16,7 @@
 *  Purpose
 *  =======
 *
-*  ZLAUUM computes the product U * U' or L' * L, where the triangular
+*  ZLAUUM computes the product U * U**H or L**H * L, where the triangular
 *  factor U or L is stored in the upper or lower triangular part of
 *  the array A.
 *
@@ -42,9 +42,9 @@
 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
 *          On entry, the triangular factor U or L.
 *          On exit, if UPLO = 'U', the upper triangle of A is
-*          overwritten with the upper triangle of the product U * U';
+*          overwritten with the upper triangle of the product U * U**H;
 *          if UPLO = 'L', the lower triangle of A is overwritten with
-*          the lower triangle of the product L' * L.
+*          the lower triangle of the product L**H * L.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -114,7 +114,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the product U * U'.
+*           Compute the product U * U**H.
 *
             DO 10 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
@@ -134,7 +134,7 @@
    10       CONTINUE
          ELSE
 *
-*           Compute the product L' * L.
+*           Compute the product L**H * L.
 *
             DO 20 I = 1, N, NB
                IB = MIN( NB, N-I+1 )
diff --git a/SRC/zpbcon.f b/SRC/zpbcon.f
index b283fbfe..880d08f4 100644
--- a/SRC/zpbcon.f
+++ b/SRC/zpbcon.f
@@ -147,7 +147,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL ZLATBS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEL, RWORK,
@@ -166,7 +166,7 @@
      $                   KD, AB, LDAB, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL ZLATBS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, KD, AB, LDAB, WORK, SCALEU, RWORK,
diff --git a/SRC/zpbsv.f b/SRC/zpbsv.f
index dd4ea901..2b9fe269 100644
--- a/SRC/zpbsv.f
+++ b/SRC/zpbsv.f
@@ -58,7 +58,7 @@
 *          See below for further details.
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U**H*U or A = L*L**H of the band
+*          Cholesky factorization A = U**H *U or A = L*L**H of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
@@ -135,7 +135,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
       CALL ZPBTRF( UPLO, N, KD, AB, LDAB, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zpbsvx.f b/SRC/zpbsvx.f
index 8861fb8c..8631a8fc 100644
--- a/SRC/zpbsvx.f
+++ b/SRC/zpbsvx.f
@@ -118,17 +118,17 @@
 *  AFB     (input or output) COMPLEX*16 array, dimension (LDAFB,N)
 *          If FACT = 'F', then AFB is an input argument and on entry
 *          contains the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the band matrix
+*          factorization A = U**H *U or A = L*L**H of the band matrix
 *          A, in the same storage format as A (see AB).  If EQUED = 'Y',
 *          then AFB is the factored form of the equilibrated matrix A.
 *
 *          If FACT = 'N', then AFB is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H.
+*          factorization A = U**H *U or A = L*L**H.
 *
 *          If FACT = 'E', then AFB is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the equilibrated
+*          factorization A = U**H *U or A = L*L**H of the equilibrated
 *          matrix A (see the description of A for the form of the
 *          equilibrated matrix).
 *
@@ -351,7 +351,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
          IF( UPPER ) THEN
             DO 40 J = 1, N
diff --git a/SRC/zpbtf2.f b/SRC/zpbtf2.f
index b06eac27..93486f98 100644
--- a/SRC/zpbtf2.f
+++ b/SRC/zpbtf2.f
@@ -20,9 +20,9 @@
 *  positive definite band matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
-*  where U is an upper triangular matrix, U' is the conjugate transpose
+*     A = U**H * U ,  if UPLO = 'U', or
+*     A = L  * L**H,  if UPLO = 'L',
+*  where U is an upper triangular matrix, U**H is the conjugate transpose
 *  of U, and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -52,7 +52,7 @@
 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
 *
 *          On exit, if INFO = 0, the triangular factor U or L from the
-*          Cholesky factorization A = U'*U or A = L*L' of the band
+*          Cholesky factorization A = U**H *U or A = L*L**H of the band
 *          matrix A, in the same storage format as A.
 *
 *  LDAB    (input) INTEGER
@@ -137,7 +137,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H * U.
 *
          DO 10 J = 1, N
 *
@@ -165,7 +165,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**H.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/zpbtrs.f b/SRC/zpbtrs.f
index 03f452b0..a732ce30 100644
--- a/SRC/zpbtrs.f
+++ b/SRC/zpbtrs.f
@@ -18,7 +18,7 @@
 *
 *  ZPBTRS solves a system of linear equations A*X = B with a Hermitian
 *  positive definite band matrix A using the Cholesky factorization
-*  A = U**H*U or A = L*L**H computed by ZPBTRF.
+*  A = U**H *U or A = L*L**H computed by ZPBTRF.
 *
 *  Arguments
 *  =========
@@ -40,7 +40,7 @@
 *
 *  AB      (input) COMPLEX*16 array, dimension (LDAB,N)
 *          The triangular factor U or L from the Cholesky factorization
-*          A = U**H*U or A = L*L**H of the band matrix A, stored in the
+*          A = U**H *U or A = L*L**H of the band matrix A, stored in the
 *          first KD+1 rows of the array.  The j-th column of U or L is
 *          stored in the j-th column of the array AB as follows:
 *          if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
@@ -107,11 +107,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H *U.
 *
          DO 10 J = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**H *X = B, overwriting B with X.
 *
             CALL ZTBSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
      $                  KD, AB, LDAB, B( 1, J ), 1 )
@@ -123,7 +123,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**H.
 *
          DO 20 J = 1, NRHS
 *
@@ -132,7 +132,7 @@
             CALL ZTBSV( 'Lower', 'No transpose', 'Non-unit', N, KD, AB,
      $                  LDAB, B( 1, J ), 1 )
 *
-*           Solve L'*X = B, overwriting B with X.
+*           Solve L**H *X = B, overwriting B with X.
 *
             CALL ZTBSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
      $                  KD, AB, LDAB, B( 1, J ), 1 )
diff --git a/SRC/zpocon.f b/SRC/zpocon.f
index 56dff353..3d5cbeef 100644
--- a/SRC/zpocon.f
+++ b/SRC/zpocon.f
@@ -136,7 +136,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL ZLATRS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SCALEL, RWORK, INFO )
@@ -154,7 +154,7 @@
      $                   A, LDA, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL ZLATRS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, A, LDA, WORK, SCALEU, RWORK, INFO )
diff --git a/SRC/zposv.f b/SRC/zposv.f
index 14a51549..f56d1d5b 100644
--- a/SRC/zposv.f
+++ b/SRC/zposv.f
@@ -53,7 +53,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H.
+*          factorization A = U**H *U or A = L*L**H.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -105,7 +105,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
       CALL ZPOTRF( UPLO, N, A, LDA, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zposvx.f b/SRC/zposvx.f
index 137b4fee..3dc5b789 100644
--- a/SRC/zposvx.f
+++ b/SRC/zposvx.f
@@ -116,18 +116,18 @@
 *  AF      (input or output) COMPLEX*16 array, dimension (LDAF,N)
 *          If FACT = 'F', then AF is an input argument and on entry
 *          contains the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H, in the same storage
+*          factorization A = U**H *U or A = L*L**H, in the same storage
 *          format as A.  If EQUED .ne. 'N', then AF is the factored form
 *          of the equilibrated matrix diag(S)*A*diag(S).
 *
 *          If FACT = 'N', then AF is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the original
+*          factorization A = U**H *U or A = L*L**H of the original
 *          matrix A.
 *
 *          If FACT = 'E', then AF is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the equilibrated
+*          factorization A = U**H *U or A = L*L**H of the equilibrated
 *          matrix A (see the description of A for the form of the
 *          equilibrated matrix).
 *
@@ -319,7 +319,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
          CALL ZLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL ZPOTRF( UPLO, N, AF, LDAF, INFO )
diff --git a/SRC/zpotf2.f b/SRC/zpotf2.f
index 549601c8..228d530a 100644
--- a/SRC/zpotf2.f
+++ b/SRC/zpotf2.f
@@ -20,8 +20,8 @@
 *  positive definite matrix A.
 *
 *  The factorization has the form
-*     A = U' * U ,  if UPLO = 'U', or
-*     A = L  * L',  if UPLO = 'L',
+*     A = U**H * U ,  if UPLO = 'U', or
+*     A = L  * L**H,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is lower triangular.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -48,7 +48,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U'*U  or A = L*L'.
+*          factorization A = U**H *U  or A = L*L**H.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -109,7 +109,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H *U.
 *
          DO 10 J = 1, N
 *
@@ -136,7 +136,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L*L**H.
 *
          DO 20 J = 1, N
 *
diff --git a/SRC/zpotrf.f b/SRC/zpotrf.f
index 5749bb03..73fec59c 100644
--- a/SRC/zpotrf.f
+++ b/SRC/zpotrf.f
@@ -46,7 +46,7 @@
 *          triangular part of A is not referenced.
 *
 *          On exit, if INFO = 0, the factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H.
+*          factorization A = U**H *U or A = L*L**H.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -117,7 +117,7 @@
 *
          IF( UPPER ) THEN
 *
-*           Compute the Cholesky factorization A = U'*U.
+*           Compute the Cholesky factorization A = U**H *U.
 *
             DO 10 J = 1, N, NB
 *
@@ -146,7 +146,7 @@
 *
          ELSE
 *
-*           Compute the Cholesky factorization A = L*L'.
+*           Compute the Cholesky factorization A = L*L**H.
 *
             DO 20 J = 1, N, NB
 *
diff --git a/SRC/zpotri.f b/SRC/zpotri.f
index 068d746b..3ebd5f52 100644
--- a/SRC/zpotri.f
+++ b/SRC/zpotri.f
@@ -86,7 +86,7 @@
       IF( INFO.GT.0 )
      $   RETURN
 *
-*     Form inv(U)*inv(U)' or inv(L)'*inv(L).
+*     Form inv(U) * inv(U)**H or inv(L)**H * inv(L).
 *
       CALL ZLAUUM( UPLO, N, A, LDA, INFO )
 *
diff --git a/SRC/zpotrs.f b/SRC/zpotrs.f
index 3ae63678..1e677855 100644
--- a/SRC/zpotrs.f
+++ b/SRC/zpotrs.f
@@ -18,7 +18,7 @@
 *
 *  ZPOTRS solves a system of linear equations A*X = B with a Hermitian
 *  positive definite matrix A using the Cholesky factorization
-*  A = U**H*U or A = L*L**H computed by ZPOTRF.
+*  A = U**H * U or A = L * L**H computed by ZPOTRF.
 *
 *  Arguments
 *  =========
@@ -36,7 +36,7 @@
 *
 *  A       (input) COMPLEX*16 array, dimension (LDA,N)
 *          The triangular factor U or L from the Cholesky factorization
-*          A = U**H*U or A = L*L**H, as computed by ZPOTRF.
+*          A = U**H * U or A = L * L**H, as computed by ZPOTRF.
 *
 *  LDA     (input) INTEGER
 *          The leading dimension of the array A.  LDA >= max(1,N).
@@ -100,9 +100,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H *U.
 *
-*        Solve U'*X = B, overwriting B with X.
+*        Solve U**H *X = B, overwriting B with X.
 *
          CALL ZTRSM( 'Left', 'Upper', 'Conjugate transpose', 'Non-unit',
      $               N, NRHS, ONE, A, LDA, B, LDB )
@@ -113,14 +113,14 @@
      $               NRHS, ONE, A, LDA, B, LDB )
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L*L**H.
 *
 *        Solve L*X = B, overwriting B with X.
 *
          CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Non-unit', N,
      $               NRHS, ONE, A, LDA, B, LDB )
 *
-*        Solve L'*X = B, overwriting B with X.
+*        Solve L**H *X = B, overwriting B with X.
 *
          CALL ZTRSM( 'Left', 'Lower', 'Conjugate transpose', 'Non-unit',
      $               N, NRHS, ONE, A, LDA, B, LDB )
diff --git a/SRC/zppcon.f b/SRC/zppcon.f
index 37136c2c..ab18a79a 100644
--- a/SRC/zppcon.f
+++ b/SRC/zppcon.f
@@ -135,7 +135,7 @@
       IF( KASE.NE.0 ) THEN
          IF( UPPER ) THEN
 *
-*           Multiply by inv(U').
+*           Multiply by inv(U**H).
 *
             CALL ZLATPS( 'Upper', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, AP, WORK, SCALEL, RWORK, INFO )
@@ -153,7 +153,7 @@
      $                   AP, WORK, SCALEL, RWORK, INFO )
             NORMIN = 'Y'
 *
-*           Multiply by inv(L').
+*           Multiply by inv(L**H).
 *
             CALL ZLATPS( 'Lower', 'Conjugate transpose', 'Non-unit',
      $                   NORMIN, N, AP, WORK, SCALEU, RWORK, INFO )
diff --git a/SRC/zppsv.f b/SRC/zppsv.f
index d4d3dfb7..27ccc9d0 100644
--- a/SRC/zppsv.f
+++ b/SRC/zppsv.f
@@ -22,7 +22,7 @@
 *  packed format and X and B are N-by-NRHS matrices.
 *
 *  The Cholesky decomposition is used to factor A as
-*     A = U**H* U,  if UPLO = 'U', or
+*     A = U**H * U,  if UPLO = 'U', or
 *     A = L * L**H,  if UPLO = 'L',
 *  where U is an upper triangular matrix and L is a lower triangular
 *  matrix.  The factored form of A is then used to solve the system of
@@ -117,7 +117,7 @@
          RETURN
       END IF
 *
-*     Compute the Cholesky factorization A = U'*U or A = L*L'.
+*     Compute the Cholesky factorization A = U**H *U or A = L*L**H.
 *
       CALL ZPPTRF( UPLO, N, AP, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zppsvx.f b/SRC/zppsvx.f
index 7e06c26f..c2cd22f4 100644
--- a/SRC/zppsvx.f
+++ b/SRC/zppsvx.f
@@ -20,7 +20,7 @@
 *  Purpose
 *  =======
 *
-*  ZPPSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to
+*  ZPPSVX uses the Cholesky factorization A = U**H * U or A = L * L**H to
 *  compute the solution to a complex system of linear equations
 *     A * X = B,
 *  where A is an N-by-N Hermitian positive definite matrix stored in
@@ -43,8 +43,8 @@
 *
 *  2. If FACT = 'N' or 'E', the Cholesky decomposition is used to
 *     factor the matrix A (after equilibration if FACT = 'E') as
-*        A = U'* U ,  if UPLO = 'U', or
-*        A = L * L',  if UPLO = 'L',
+*        A = U**H * U ,  if UPLO = 'U', or
+*        A = L * L**H,  if UPLO = 'L',
 *     where U is an upper triangular matrix, L is a lower triangular
 *     matrix, and ' indicates conjugate transpose.
 *
@@ -117,12 +117,12 @@
 *
 *          If FACT = 'N', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the original
+*          factorization A = U**H * U or A = L * L**H of the original
 *          matrix A.
 *
 *          If FACT = 'E', then AFP is an output argument and on exit
 *          returns the triangular factor U or L from the Cholesky
-*          factorization A = U**H*U or A = L*L**H of the equilibrated
+*          factorization A = U**H * U or A = L * L**H of the equilibrated
 *          matrix A (see the description of AP for the form of the
 *          equilibrated matrix).
 *
@@ -324,7 +324,7 @@
 *
       IF( NOFACT .OR. EQUIL ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U or A = L*L'.
+*        Compute the Cholesky factorization A = U**H * U or A = L * L**H.
 *
          CALL ZCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL ZPPTRF( UPLO, N, AFP, INFO )
diff --git a/SRC/zpptrf.f b/SRC/zpptrf.f
index a1631ceb..89a9590f 100644
--- a/SRC/zpptrf.f
+++ b/SRC/zpptrf.f
@@ -115,7 +115,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute the Cholesky factorization A = U'*U.
+*        Compute the Cholesky factorization A = U**H * U.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -140,7 +140,7 @@
    10    CONTINUE
       ELSE
 *
-*        Compute the Cholesky factorization A = L*L'.
+*        Compute the Cholesky factorization A = L * L**H.
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/zpptri.f b/SRC/zpptri.f
index bc0d68d1..58959bb2 100644
--- a/SRC/zpptri.f
+++ b/SRC/zpptri.f
@@ -97,7 +97,7 @@
      $   RETURN
       IF( UPPER ) THEN
 *
-*        Compute the product inv(U) * inv(U)'.
+*        Compute the product inv(U) * inv(U)**H.
 *
          JJ = 0
          DO 10 J = 1, N
@@ -111,7 +111,7 @@
 *
       ELSE
 *
-*        Compute the product inv(L)' * inv(L).
+*        Compute the product inv(L)**H * inv(L).
 *
          JJ = 1
          DO 20 J = 1, N
diff --git a/SRC/zpptrs.f b/SRC/zpptrs.f
index ef322f07..93a821e2 100644
--- a/SRC/zpptrs.f
+++ b/SRC/zpptrs.f
@@ -18,7 +18,7 @@
 *
 *  ZPPTRS solves a system of linear equations A*X = B with a Hermitian
 *  positive definite matrix A in packed storage using the Cholesky
-*  factorization A = U**H*U or A = L*L**H computed by ZPPTRF.
+*  factorization A = U**H * U or A = L * L**H computed by ZPPTRF.
 *
 *  Arguments
 *  =========
@@ -36,7 +36,7 @@
 *
 *  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
 *          The triangular factor U or L from the Cholesky factorization
-*          A = U**H*U or A = L*L**H, packed columnwise in a linear
+*          A = U**H * U or A = L * L**H, packed columnwise in a linear
 *          array.  The j-th column of U or L is stored in the array AP
 *          as follows:
 *          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
@@ -96,11 +96,11 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B where A = U'*U.
+*        Solve A*X = B where A = U**H * U.
 *
          DO 10 I = 1, NRHS
 *
-*           Solve U'*X = B, overwriting B with X.
+*           Solve U**H *X = B, overwriting B with X.
 *
             CALL ZTPSV( 'Upper', 'Conjugate transpose', 'Non-unit', N,
      $                  AP, B( 1, I ), 1 )
@@ -112,7 +112,7 @@
    10    CONTINUE
       ELSE
 *
-*        Solve A*X = B where A = L*L'.
+*        Solve A*X = B where A = L * L**H.
 *
          DO 20 I = 1, NRHS
 *
@@ -121,7 +121,7 @@
             CALL ZTPSV( 'Lower', 'No transpose', 'Non-unit', N, AP,
      $                  B( 1, I ), 1 )
 *
-*           Solve L'*X = Y, overwriting B with X.
+*           Solve L**H *X = Y, overwriting B with X.
 *
             CALL ZTPSV( 'Lower', 'Conjugate transpose', 'Non-unit', N,
      $                  AP, B( 1, I ), 1 )
diff --git a/SRC/zptcon.f b/SRC/zptcon.f
index 43541b51..4c7992b0 100644
--- a/SRC/zptcon.f
+++ b/SRC/zptcon.f
@@ -118,7 +118,7 @@
 *        m(i,j) =  abs(A(i,j)), i = j,
 *        m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**H.
 *
 *     Solve M(L) * x = e.
 *
@@ -127,7 +127,7 @@
          RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )
    20 CONTINUE
 *
-*     Solve D * M(L)' * x = b.
+*     Solve D * M(L)**H * x = b.
 *
       RWORK( N ) = RWORK( N ) / D( N )
       DO 30 I = N - 1, 1, -1
diff --git a/SRC/zptrfs.f b/SRC/zptrfs.f
index ba6dde63..90577ca9 100644
--- a/SRC/zptrfs.f
+++ b/SRC/zptrfs.f
@@ -327,7 +327,7 @@
 *           m(i,j) =  abs(A(i,j)), i = j,
 *           m(i,j) = -abs(A(i,j)), i .ne. j,
 *
-*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
+*        and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)**H.
 *
 *        Solve M(L) * x = e.
 *
@@ -336,7 +336,7 @@
             RWORK( I ) = ONE + RWORK( I-1 )*ABS( EF( I-1 ) )
    70    CONTINUE
 *
-*        Solve D * M(L)' * x = b.
+*        Solve D * M(L)**H * x = b.
 *
          RWORK( N ) = RWORK( N ) / DF( N )
          DO 80 I = N - 1, 1, -1
diff --git a/SRC/zptsv.f b/SRC/zptsv.f
index 8aee5cbe..246f7c76 100644
--- a/SRC/zptsv.f
+++ b/SRC/zptsv.f
@@ -45,7 +45,7 @@
 *          A.  E can also be regarded as the superdiagonal of the unit
 *          bidiagonal factor U from the U**H*D*U factorization of A.
 *
-*  B       (input/output) COMPLEX*16 array, dimension (LDB,N)
+*  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
 *          On entry, the N-by-NRHS right hand side matrix B.
 *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
 *
@@ -85,7 +85,7 @@
          RETURN
       END IF
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**H (or U**H*D*U) factorization of A.
 *
       CALL ZPTTRF( N, D, E, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zptsvx.f b/SRC/zptsvx.f
index 7f782cbc..d933c443 100644
--- a/SRC/zptsvx.f
+++ b/SRC/zptsvx.f
@@ -191,7 +191,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the L*D*L' (or U'*D*U) factorization of A.
+*        Compute the L*D*L**H (or U**H*D*U) factorization of A.
 *
          CALL DCOPY( N, D, 1, DF, 1 )
          IF( N.GT.1 )
diff --git a/SRC/zpttrf.f b/SRC/zpttrf.f
index 20879ce5..fca677dc 100644
--- a/SRC/zpttrf.f
+++ b/SRC/zpttrf.f
@@ -16,9 +16,9 @@
 *  Purpose
 *  =======
 *
-*  ZPTTRF computes the L*D*L' factorization of a complex Hermitian
+*  ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
 *  positive definite tridiagonal matrix A.  The factorization may also
-*  be regarded as having the form A = U'*D*U.
+*  be regarded as having the form A = U**H *D*U.
 *
 *  Arguments
 *  =========
@@ -29,14 +29,14 @@
 *  D       (input/output) DOUBLE PRECISION array, dimension (N)
 *          On entry, the n diagonal elements of the tridiagonal matrix
 *          A.  On exit, the n diagonal elements of the diagonal matrix
-*          D from the L*D*L' factorization of A.
+*          D from the L*D*L**H factorization of A.
 *
 *  E       (input/output) COMPLEX*16 array, dimension (N-1)
 *          On entry, the (n-1) subdiagonal elements of the tridiagonal
 *          matrix A.  On exit, the (n-1) subdiagonal elements of the
-*          unit bidiagonal factor L from the L*D*L' factorization of A.
+*          unit bidiagonal factor L from the L*D*L**H factorization of A.
 *          E can also be regarded as the superdiagonal of the unit
-*          bidiagonal factor U from the U'*D*U factorization of A.
+*          bidiagonal factor U from the U**H *D*U factorization of A.
 *
 *  INFO    (output) INTEGER
 *          = 0: successful exit
@@ -78,7 +78,7 @@
       IF( N.EQ.0 )
      $   RETURN
 *
-*     Compute the L*D*L' (or U'*D*U) factorization of A.
+*     Compute the L*D*L**H (or U**H *D*U) factorization of A.
 *
       I4 = MOD( N-1, 4 )
       DO 10 I = 1, I4
diff --git a/SRC/zpttrs.f b/SRC/zpttrs.f
index 988aa43a..667e543b 100644
--- a/SRC/zpttrs.f
+++ b/SRC/zpttrs.f
@@ -19,7 +19,7 @@
 *
 *  ZPTTRS solves a tridiagonal system of the form
 *     A * X = B
-*  using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF.
+*  using the factorization A = U**H *D* U or A = L*D*L**H computed by ZPTTRF.
 *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
 *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 *  the vector E, and X and B are N by NRHS matrices.
@@ -31,8 +31,8 @@
 *          Specifies the form of the factorization and whether the
 *          vector E is the superdiagonal of the upper bidiagonal factor
 *          U or the subdiagonal of the lower bidiagonal factor L.
-*          = 'U':  A = U'*D*U, E is the superdiagonal of U
-*          = 'L':  A = L*D*L', E is the subdiagonal of L
+*          = 'U':  A = U**H *D*U, E is the superdiagonal of U
+*          = 'L':  A = L*D*L**H, E is the subdiagonal of L
 *
 *  N       (input) INTEGER
 *          The order of the tridiagonal matrix A.  N >= 0.
@@ -43,13 +43,13 @@
 *
 *  D       (input) DOUBLE PRECISION array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          factorization A = U'*D*U or A = L*D*L'.
+*          factorization A = U**H *D*U or A = L*D*L**H.
 *
 *  E       (input) COMPLEX*16 array, dimension (N-1)
 *          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
-*          bidiagonal factor U from the factorization A = U'*D*U.
+*          bidiagonal factor U from the factorization A = U**H*D*U.
 *          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
-*          bidiagonal factor L from the factorization A = L*D*L'.
+*          bidiagonal factor L from the factorization A = L*D*L**H.
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
diff --git a/SRC/zptts2.f b/SRC/zptts2.f
index 39b86590..d8701b69 100644
--- a/SRC/zptts2.f
+++ b/SRC/zptts2.f
@@ -18,7 +18,7 @@
 *
 *  ZPTTS2 solves a tridiagonal system of the form
 *     A * X = B
-*  using the factorization A = U'*D*U or A = L*D*L' computed by ZPTTRF.
+*  using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
 *  D is a diagonal matrix specified in the vector D, U (or L) is a unit
 *  bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 *  the vector E, and X and B are N by NRHS matrices.
@@ -30,8 +30,8 @@
 *          Specifies the form of the factorization and whether the
 *          vector E is the superdiagonal of the upper bidiagonal factor
 *          U or the subdiagonal of the lower bidiagonal factor L.
-*          = 1:  A = U'*D*U, E is the superdiagonal of U
-*          = 0:  A = L*D*L', E is the subdiagonal of L
+*          = 1:  A = U**H *D*U, E is the superdiagonal of U
+*          = 0:  A = L*D*L**H, E is the subdiagonal of L
 *
 *  N       (input) INTEGER
 *          The order of the tridiagonal matrix A.  N >= 0.
@@ -42,13 +42,13 @@
 *
 *  D       (input) DOUBLE PRECISION array, dimension (N)
 *          The n diagonal elements of the diagonal matrix D from the
-*          factorization A = U'*D*U or A = L*D*L'.
+*          factorization A = U**H *D*U or A = L*D*L**H.
 *
 *  E       (input) COMPLEX*16 array, dimension (N-1)
 *          If IUPLO = 1, the (n-1) superdiagonal elements of the unit
-*          bidiagonal factor U from the factorization A = U'*D*U.
+*          bidiagonal factor U from the factorization A = U**H*D*U.
 *          If IUPLO = 0, the (n-1) subdiagonal elements of the unit
-*          bidiagonal factor L from the factorization A = L*D*L'.
+*          bidiagonal factor L from the factorization A = L*D*L**H.
 *
 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
 *          On entry, the right hand side vectors B for the system of
@@ -81,14 +81,14 @@
 *
       IF( IUPLO.EQ.1 ) THEN
 *
-*        Solve A * X = B using the factorization A = U'*D*U,
+*        Solve A * X = B using the factorization A = U**H *D*U,
 *        overwriting each right hand side vector with its solution.
 *
          IF( NRHS.LE.2 ) THEN
             J = 1
    10       CONTINUE
 *
-*           Solve U' * x = b.
+*           Solve U**H * x = b.
 *
             DO 20 I = 2, N
                B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
@@ -109,7 +109,7 @@
          ELSE
             DO 70 J = 1, NRHS
 *
-*              Solve U' * x = b.
+*              Solve U**H * x = b.
 *
                DO 50 I = 2, N
                   B( I, J ) = B( I, J ) - B( I-1, J )*DCONJG( E( I-1 ) )
@@ -125,7 +125,7 @@
          END IF
       ELSE
 *
-*        Solve A * X = B using the factorization A = L*D*L',
+*        Solve A * X = B using the factorization A = L*D*L**H,
 *        overwriting each right hand side vector with its solution.
 *
          IF( NRHS.LE.2 ) THEN
@@ -138,7 +138,7 @@
                B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
    90       CONTINUE
 *
-*           Solve D * L' * x = b.
+*           Solve D * L**H * x = b.
 *
             DO 100 I = 1, N
                B( I, J ) = B( I, J ) / D( I )
@@ -159,7 +159,7 @@
                   B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
   120          CONTINUE
 *
-*              Solve D * L' * x = b.
+*              Solve D * L**H * x = b.
 *
                B( N, J ) = B( N, J ) / D( N )
                DO 130 I = N - 1, 1, -1
diff --git a/SRC/zspcon.f b/SRC/zspcon.f
index 437f0b6b..b065a766 100644
--- a/SRC/zspcon.f
+++ b/SRC/zspcon.f
@@ -142,7 +142,7 @@
       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL ZSPTRS( UPLO, N, 1, AP, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/zspsv.f b/SRC/zspsv.f
index fcbdc72d..60474253 100644
--- a/SRC/zspsv.f
+++ b/SRC/zspsv.f
@@ -132,7 +132,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL ZSPTRF( UPLO, N, AP, IPIV, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zspsvx.f b/SRC/zspsvx.f
index 4289a488..6505d51f 100644
--- a/SRC/zspsvx.f
+++ b/SRC/zspsvx.f
@@ -234,7 +234,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL ZCOPY( N*( N+1 ) / 2, AP, 1, AFP, 1 )
          CALL ZSPTRF( UPLO, N, AFP, IPIV, INFO )
diff --git a/SRC/zsptrf.f b/SRC/zsptrf.f
index 408de266..752b16b0 100644
--- a/SRC/zsptrf.f
+++ b/SRC/zsptrf.f
@@ -72,7 +72,7 @@
 *  5-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -89,7 +89,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -162,7 +162,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -283,7 +283,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = CONE / AP( KC+K-1 )
                CALL ZSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
@@ -302,8 +302,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -348,7 +348,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -476,7 +476,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = CONE / AP( KC )
                   CALL ZSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
@@ -499,8 +499,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/zsptri.f b/SRC/zsptri.f
index c7f24854..5491f997 100644
--- a/SRC/zsptri.f
+++ b/SRC/zsptri.f
@@ -128,7 +128,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -229,7 +229,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/zsptrs.f b/SRC/zsptrs.f
index 546f5c02..2fc812bf 100644
--- a/SRC/zsptrs.f
+++ b/SRC/zsptrs.f
@@ -103,7 +103,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -177,7 +177,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -212,7 +212,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
@@ -234,7 +234,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -311,7 +311,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T*X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -330,7 +330,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -347,7 +347,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/zsycon.f b/SRC/zsycon.f
index 4749e2b7..adf2a05f 100644
--- a/SRC/zsycon.f
+++ b/SRC/zsycon.f
@@ -146,7 +146,7 @@
       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
       IF( KASE.NE.0 ) THEN
 *
-*        Multiply by inv(L*D*L') or inv(U*D*U').
+*        Multiply by inv(L*D*L**T) or inv(U*D*U**T).
 *
          CALL ZSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
          GO TO 30
diff --git a/SRC/zsysv.f b/SRC/zsysv.f
index d5e81c8d..7794f607 100644
--- a/SRC/zsysv.f
+++ b/SRC/zsysv.f
@@ -158,7 +158,7 @@
          RETURN
       END IF
 *
-*     Compute the factorization A = U*D*U' or A = L*D*L'.
+*     Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
       CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
       IF( INFO.EQ.0 ) THEN
diff --git a/SRC/zsysvx.f b/SRC/zsysvx.f
index 859dbd60..0a97d32b 100644
--- a/SRC/zsysvx.f
+++ b/SRC/zsysvx.f
@@ -255,7 +255,7 @@
 *
       IF( NOFACT ) THEN
 *
-*        Compute the factorization A = U*D*U' or A = L*D*L'.
+*        Compute the factorization A = U*D*U**T or A = L*D*L**T.
 *
          CALL ZLACPY( UPLO, N, N, A, LDA, AF, LDAF )
          CALL ZSYTRF( UPLO, N, AF, LDAF, IPIV, WORK, LWORK, INFO )
diff --git a/SRC/zsytf2.f b/SRC/zsytf2.f
index 9d9e4d7e..abecad11 100644
--- a/SRC/zsytf2.f
+++ b/SRC/zsytf2.f
@@ -20,10 +20,10 @@
 *  ZSYTF2 computes the factorization of a complex symmetric matrix A
 *  using the Bunch-Kaufman diagonal pivoting method:
 *
-*     A = U*D*U'  or  A = L*D*L'
+*     A = U*D*U**T  or  A = L*D*L**T
 *
 *  where U (or L) is a product of permutation and unit upper (lower)
-*  triangular matrices, U' is the transpose of U, and D is symmetric and
+*  triangular matrices, U**T is the transpose of U, and D is symmetric and
 *  block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
 *
 *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
@@ -87,7 +87,7 @@
 *  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
 *         Company
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -178,7 +178,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2
@@ -209,7 +209,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or NaN: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -284,7 +284,7 @@
 *
 *              Perform a rank-1 update of A(1:k-1,1:k-1) as
 *
-*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)'
+*              A := A - U(k)*D(k)*U(k)**T = A - W(k)*1/D(k)*W(k)**T
 *
                R1 = CONE / A( K, K )
                CALL ZSYR( UPLO, K-1, -R1, A( 1, K ), 1, A, LDA )
@@ -303,8 +303,8 @@
 *
 *              Perform a rank-2 update of A(1:k-2,1:k-2) as
 *
-*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )'
-*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )'
+*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
 *
                IF( K.GT.2 ) THEN
 *
@@ -346,7 +346,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2
@@ -377,7 +377,7 @@
 *
          IF( MAX( ABSAKK, COLMAX ).EQ.ZERO .OR. DISNAN(ABSAKK) ) THEN
 *
-*           Column K is zero or contains a NaN: set INFO and continue
+*           Column K is zero or NaN: set INFO and continue
 *
             IF( INFO.EQ.0 )
      $         INFO = K
@@ -455,7 +455,7 @@
 *
 *                 Perform a rank-1 update of A(k+1:n,k+1:n) as
 *
-*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)'
+*                 A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
 *
                   R1 = CONE / A( K, K )
                   CALL ZSYR( UPLO, N-K, -R1, A( K+1, K ), 1,
@@ -473,8 +473,8 @@
 *
 *                 Perform a rank-2 update of A(k+2:n,k+2:n) as
 *
-*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )'
-*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )'
+*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )**T
+*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
 *
 *                 where L(k) and L(k+1) are the k-th and (k+1)-th
 *                 columns of L
diff --git a/SRC/zsytrf.f b/SRC/zsytrf.f
index b6087999..6687826a 100644
--- a/SRC/zsytrf.f
+++ b/SRC/zsytrf.f
@@ -87,7 +87,7 @@
 *  Further Details
 *  ===============
 *
-*  If UPLO = 'U', then A = U*D*U', where
+*  If UPLO = 'U', then A = U*D*U**T, where
 *     U = P(n)*U(n)* ... *P(k)U(k)* ...,
 *  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
 *  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -104,7 +104,7 @@
 *  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
 *  and A(k,k), and v overwrites A(1:k-2,k-1:k).
 *
-*  If UPLO = 'L', then A = L*D*L', where
+*  If UPLO = 'L', then A = L*D*L**T, where
 *     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
 *  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
 *  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
@@ -187,7 +187,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Factorize A as U*D*U' using the upper triangle of A
+*        Factorize A as U*D*U**T using the upper triangle of A
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        KB, where KB is the number of columns factorized by ZLASYF;
@@ -227,7 +227,7 @@
 *
       ELSE
 *
-*        Factorize A as L*D*L' using the lower triangle of A
+*        Factorize A as L*D*L**T using the lower triangle of A
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        KB, where KB is the number of columns factorized by ZLASYF;
diff --git a/SRC/zsytri.f b/SRC/zsytri.f
index b2e6ab6c..73be67c1 100644
--- a/SRC/zsytri.f
+++ b/SRC/zsytri.f
@@ -128,7 +128,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Compute inv(A) from the factorization A = U*D*U'.
+*        Compute inv(A) from the factorization A = U*D*U**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -217,7 +217,7 @@
 *
       ELSE
 *
-*        Compute inv(A) from the factorization A = L*D*L'.
+*        Compute inv(A) from the factorization A = L*D*L**T.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
diff --git a/SRC/zsytri2x.f b/SRC/zsytri2x.f
index 41cffcb2..c39e4175 100644
--- a/SRC/zsytri2x.f
+++ b/SRC/zsytri2x.f
@@ -154,7 +154,7 @@
 
       IF( UPPER ) THEN
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
         CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -182,9 +182,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=N
         DO WHILE (CUT .GT. 0)
@@ -309,7 +309,7 @@
 *
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 *  
             I=1
             DO WHILE ( I .LE. N )
@@ -331,7 +331,7 @@
 *
 *        LOWER...
 *
-*        invA = P * inv(U')*inv(D)*inv(U)*P'.
+*        invA = P * inv(U**T)*inv(D)*inv(U)*P'.
 *
          CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO )
 *
@@ -359,9 +359,9 @@
          END IF
         END DO
 *
-*       inv(U') = (inv(U))'
+*       inv(U**T) = (inv(U))**T
 *
-*       inv(U')*inv(D)*inv(U)
+*       inv(U**T)*inv(D)*inv(U)
 *
         CUT=0
         DO WHILE (CUT .LT. N)
@@ -493,7 +493,7 @@
            CUT=CUT+NNB
        END DO
 *
-*        Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P'
+*        Apply PERMUTATIONS P and P': P * inv(U**T)*inv(D)*inv(U) *P'
 * 
             I=N
             DO WHILE ( I .GE. 1 )
diff --git a/SRC/zsytrs.f b/SRC/zsytrs.f
index f8ce8dfa..7ccee7cc 100644
--- a/SRC/zsytrs.f
+++ b/SRC/zsytrs.f
@@ -107,7 +107,7 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
 *        First solve U*D*X = B, overwriting B with X.
 *
@@ -178,7 +178,7 @@
          GO TO 10
    30    CONTINUE
 *
-*        Next solve U'*X = B, overwriting B with X.
+*        Next solve U**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, increasing from 1 to N in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -195,7 +195,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(U'(K)), where U(K) is the transformation
+*           Multiply by inv(U**T(K)), where U(K) is the transformation
 *           stored in column K of A.
 *
             CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -211,7 +211,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+*           Multiply by inv(U**T(K+1)), where U(K+1) is the transformation
 *           stored in columns K and K+1 of A.
 *
             CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
@@ -232,7 +232,7 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
 *        First solve L*D*X = B, overwriting B with X.
 *
@@ -306,7 +306,7 @@
          GO TO 60
    80    CONTINUE
 *
-*        Next solve L'*X = B, overwriting B with X.
+*        Next solve L**T *X = B, overwriting B with X.
 *
 *        K is the main loop index, decreasing from N to 1 in steps of
 *        1 or 2, depending on the size of the diagonal blocks.
@@ -323,7 +323,7 @@
 *
 *           1 x 1 diagonal block
 *
-*           Multiply by inv(L'(K)), where L(K) is the transformation
+*           Multiply by inv(L**T(K)), where L(K) is the transformation
 *           stored in column K of A.
 *
             IF( K.LT.N )
@@ -340,7 +340,7 @@
 *
 *           2 x 2 diagonal block
 *
-*           Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+*           Multiply by inv(L**T(K-1)), where L(K-1) is the transformation
 *           stored in columns K-1 and K of A.
 *
             IF( K.LT.N ) THEN
diff --git a/SRC/zsytrs2.f b/SRC/zsytrs2.f
index 31441e58..8588ec49 100644
--- a/SRC/zsytrs2.f
+++ b/SRC/zsytrs2.f
@@ -117,9 +117,9 @@
 *
       IF( UPPER ) THEN
 *
-*        Solve A*X = B, where A = U*D*U'.
+*        Solve A*X = B, where A = U*D*U**T.
 *
-*       P' * B  
+*       P**T * B  
         K=N
         DO WHILE ( K .GE. 1 )
          IF( IPIV( K ).GT.0 ) THEN
@@ -139,11 +139,11 @@
          END IF
         END DO
 *
-*  Compute (U \P' * B) -> B    [ (U \P' * B) ]
+*  Compute (U \P**T * B) -> B    [ (U \P**T * B) ]
 *
         CALL ZTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (U \P' * B) ]
+*  Compute D \ B -> B   [ D \ (U \P**T * B) ]
 *       
          I=N
          DO WHILE ( I .GE. 1 )
@@ -167,11 +167,11 @@
             I = I - 1
          END DO
 *
-*      Compute (U' \ B) -> B   [ U' \ (D \ (U \P' * B) ) ]
+*      Compute (U**T \ B) -> B   [ U**T \ (D \ (U \P**T * B) ) ]
 *
          CALL ZTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (U' \ (D \ (U \P' * B) )) ]
+*       P * B  [ P * (U**T \ (D \ (U \P**T * B) )) ]
 *
         K=1
         DO WHILE ( K .LE. N )
@@ -194,9 +194,9 @@
 *
       ELSE
 *
-*        Solve A*X = B, where A = L*D*L'.
+*        Solve A*X = B, where A = L*D*L**T.
 *
-*       P' * B  
+*       P**T * B  
         K=1
         DO WHILE ( K .LE. N )
          IF( IPIV( K ).GT.0 ) THEN
@@ -216,11 +216,11 @@
          ENDIF
         END DO
 *
-*  Compute (L \P' * B) -> B    [ (L \P' * B) ]
+*  Compute (L \P**T * B) -> B    [ (L \P**T * B) ]
 *
         CALL ZTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*  Compute D \ B -> B   [ D \ (L \P' * B) ]
+*  Compute D \ B -> B   [ D \ (L \P**T * B) ]
 *       
          I=1
          DO WHILE ( I .LE. N )
@@ -242,11 +242,11 @@
             I = I + 1
          END DO
 *
-*  Compute (L' \ B) -> B   [ L' \ (D \ (L \P' * B) ) ]
+*  Compute (L**T \ B) -> B   [ L**T \ (D \ (L \P**T * B) ) ]
 * 
         CALL ZTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB)
 *
-*       P * B  [ P * (L' \ (D \ (L \P' * B) )) ]
+*       P * B  [ P * (L**T \ (D \ (L \P**T * B) )) ]
 *
         K=N
         DO WHILE ( K .GE. 1 )
diff --git a/SRC/ztgex2.f b/SRC/ztgex2.f
index a715c1a6..d672e43e 100644
--- a/SRC/ztgex2.f
+++ b/SRC/ztgex2.f
@@ -28,8 +28,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
+*         Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
 *
 *
 *  Arguments
@@ -213,7 +213,7 @@
       IF( WANDS ) THEN
 *
 *        Strong stability test:
-*           F-norm((A-QL'*S*QR, B-QL'*T*QR)) <= O(EPS*F-norm((A, B)))
+*           F-norm((A-QL**H*S*QR, B-QL**H*T*QR)) <= O(EPS*F-norm((A, B)))
 *
          CALL ZLACPY( 'Full', M, M, S, LDST, WORK, M )
          CALL ZLACPY( 'Full', M, M, T, LDST, WORK( M*M+1 ), M )
diff --git a/SRC/ztgexc.f b/SRC/ztgexc.f
index ce632369..d5668359 100644
--- a/SRC/ztgexc.f
+++ b/SRC/ztgexc.f
@@ -29,8 +29,8 @@
 *  Optionally, the matrices Q and Z of generalized Schur vectors are
 *  updated.
 *
-*         Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
-*         Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
+*         Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
+*         Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
 *
 *  Arguments
 *  =========
diff --git a/SRC/ztgsen.f b/SRC/ztgsen.f
index 0e8736f5..70a0d48d 100644
--- a/SRC/ztgsen.f
+++ b/SRC/ztgsen.f
@@ -28,7 +28,7 @@
 *
 *  ZTGSEN reorders the generalized Schur decomposition of a complex
 *  matrix pair (A, B) (in terms of an unitary equivalence trans-
-*  formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues
+*  formation Q**H * (A, B) * Z), so that a selected cluster of eigenvalues
 *  appears in the leading diagonal blocks of the pair (A,B). The leading
 *  columns of Q and Z form unitary bases of the corresponding left and
 *  right eigenspaces (deflating subspaces). (A, B) must be in
@@ -197,19 +197,19 @@
 *  U and W that move them to the top left corner of (A, B). In other
 *  words, the selected eigenvalues are the eigenvalues of (A11, B11) in
 *
-*                U'*(A, B)*W = (A11 A12) (B11 B12) n1
+*              U**H*(A, B)*W = (A11 A12) (B11 B12) n1
 *                              ( 0  A22),( 0  B22) n2
 *                                n1  n2    n1  n2
 *
-*  where N = n1+n2 and U' means the conjugate transpose of U. The first
+*  where N = n1+n2 and U**H means the conjugate transpose of U. The first
 *  n1 columns of U and W span the specified pair of left and right
 *  eigenspaces (deflating subspaces) of (A, B).
 *
 *  If (A, B) has been obtained from the generalized real Schur
-*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the
+*  decomposition of a matrix pair (C, D) = Q*(A, B)*Z**H, then the
 *  reordered generalized Schur form of (C, D) is given by
 *
-*           (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',
+*           (C, D) = (Q*U)*(U**H *(A, B)*W)*(Z*W)**H,
 *
 *  and the first n1 columns of Q*U and Z*W span the corresponding
 *  deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).
diff --git a/SRC/ztgsja.f b/SRC/ztgsja.f
index e9ca0a34..3a0ed1a0 100644
--- a/SRC/ztgsja.f
+++ b/SRC/ztgsja.f
@@ -48,10 +48,10 @@
 *
 *  On exit,
 *
-*         U'*A*Q = D1*( 0 R ),    V'*B*Q = D2*( 0 R ),
+*         U**H *A*Q = D1*( 0 R ),    V**H *B*Q = D2*( 0 R ),
 *
-*  where U, V and Q are unitary matrices, Z' denotes the conjugate
-*  transpose of Z, R is a nonsingular upper triangular matrix, and D1
+*  where U, V and Q are unitary matrices.
+*  R is a nonsingular upper triangular matrix, and D1
 *  and D2 are ``diagonal'' matrices, which are of the following
 *  structures:
 *
@@ -184,7 +184,7 @@
 *            ALPHA(K+1:M)= C, ALPHA(M+1:K+L)= 0
 *            BETA(K+1:M) = S, BETA(M+1:K+L) = 1.
 *          Furthermore, if K+L < N,
-*            ALPHA(K+L+1:N) = 0
+*            ALPHA(K+L+1:N) = 0 and
 *            BETA(K+L+1:N)  = 0.
 *
 *  U       (input/output) COMPLEX*16 array, dimension (LDU,M)
@@ -248,10 +248,10 @@
 *  min(L,M-K)-by-L triangular (or trapezoidal) matrix A23 and L-by-L
 *  matrix B13 to the form:
 *
-*           U1'*A13*Q1 = C1*R1; V1'*B13*Q1 = S1*R1,
+*           U1**H *A13*Q1 = C1*R1; V1**H *B13*Q1 = S1*R1,
 *
-*  where U1, V1 and Q1 are unitary matrix, and Z' is the conjugate
-*  transpose of Z.  C1 and S1 are diagonal matrices satisfying
+*  where U1, V1 and Q1 are unitary matrix.
+*  C1 and S1 are diagonal matrices satisfying
 *
 *                C1**2 + S1**2 = I,
 *
@@ -372,13 +372,13 @@
                CALL ZLAGS2( UPPER, A1, A2, A3, B1, B2, B3, CSU, SNU,
      $                      CSV, SNV, CSQ, SNQ )
 *
-*              Update (K+I)-th and (K+J)-th rows of matrix A: U'*A
+*              Update (K+I)-th and (K+J)-th rows of matrix A: U**H *A
 *
                IF( K+J.LE.M )
      $            CALL ZROT( L, A( K+J, N-L+1 ), LDA, A( K+I, N-L+1 ),
      $                       LDA, CSU, DCONJG( SNU ) )
 *
-*              Update I-th and J-th rows of matrix B: V'*B
+*              Update I-th and J-th rows of matrix B: V**H *B
 *
                CALL ZROT( L, B( J, N-L+1 ), LDB, B( I, N-L+1 ), LDB,
      $                    CSV, DCONJG( SNV ) )
@@ -495,6 +495,7 @@
             END IF
 *
          ELSE
+*
             ALPHA( K+I ) = ZERO
             BETA( K+I ) = ONE
             CALL ZCOPY( L-I+1, B( I, N-L+I ), LDB, A( K+I, N-L+I ),
diff --git a/SRC/ztgsna.f b/SRC/ztgsna.f
index f4132a48..02d07e94 100644
--- a/SRC/ztgsna.f
+++ b/SRC/ztgsna.f
@@ -132,12 +132,12 @@
 *  The reciprocal of the condition number of the i-th generalized
 *  eigenvalue w = (a, b) is defined as
 *
-*          S(I) = (|v'Au|**2 + |v'Bu|**2)**(1/2) / (norm(u)*norm(v))
+*          S(I) = (|v**HAu|**2 + |v**HBu|**2)**(1/2) / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of (A, B)
 *  corresponding to w; |z| denotes the absolute value of the complex
 *  number, and norm(u) denotes the 2-norm of the vector u. The pair
-*  (a, b) corresponds to an eigenvalue w = a/b (= v'Au/v'Bu) of the
+*  (a, b) corresponds to an eigenvalue w = a/b (= v**HAu/v**HBu) of the
 *  matrix pair (A, B). If both a and b equal zero, then (A,B) is
 *  singular and S(I) = -1 is returned.
 *
@@ -166,7 +166,7 @@
 *         Zl = [ kron(a, In-1) -kron(1, A22) ]
 *              [ kron(b, In-1) -kron(1, B22) ].
 *
-*  Here In-1 is the identity matrix of size n-1 and X' is the conjugate
+*  Here In-1 is the identity matrix of size n-1 and X**H is the conjugate
 *  transpose of X. kron(X, Y) is the Kronecker product between the
 *  matrices X and Y.
 *
diff --git a/SRC/ztgsy2.f b/SRC/ztgsy2.f
index bcf692b6..f91363ad 100644
--- a/SRC/ztgsy2.f
+++ b/SRC/ztgsy2.f
@@ -298,7 +298,7 @@
       ELSE
 *
 *        Solve transposed (I, J) - system:
-*           A(I, I)' * R(I, J) + D(I, I)' * L(J, J) = C(I, J)
+*           A(I, I)**H * R(I, J) + D(I, I)**H * L(J, J) = C(I, J)
 *           R(I, I) * B(J, J) + L(I, J) * E(J, J)   = -F(I, J)
 *        for I = 1, 2, ..., M, J = N, N - 1, ..., 1
 *
diff --git a/SRC/ztgsyl.f b/SRC/ztgsyl.f
index f9e2bfc8..7548bbbd 100644
--- a/SRC/ztgsyl.f
+++ b/SRC/ztgsyl.f
@@ -46,11 +46,11 @@
 *  transpose of X. Kron(X, Y) is the Kronecker product between the
 *  matrices X and Y.
 *
-*  If TRANS = 'C', y in the conjugate transposed system Z'*y = scale*b
+*  If TRANS = 'C', y in the conjugate transposed system Z**H *y = scale*b
 *  is solved for, which is equivalent to solve for R and L in
 *
-*              A' * R + D' * L = scale * C           (3)
-*              R * B' + L * E' = scale * -F
+*              A**H * R + D**H * L = scale * C           (3)
+*              R * B**H + L * E**H = scale * -F
 *
 *  This case (TRANS = 'C') is used to compute an one-norm-based estimate
 *  of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
@@ -492,7 +492,7 @@
       ELSE
 *
 *        Solve transposed (I, J)-subsystem
-*            A(I, I)' * R(I, J) + D(I, I)' * L(I, J) = C(I, J)
+*            A(I, I)**H * R(I, J) + D(I, I)**H * L(I, J) = C(I, J)
 *            R(I, J) * B(J, J)  + L(I, J) * E(J, J) = -F(I, J)
 *        for I = 1,2,..., P; J = Q, Q-1,..., 1
 *
diff --git a/SRC/ztrevc.f b/SRC/ztrevc.f
index bd4473d8..2558fddf 100644
--- a/SRC/ztrevc.f
+++ b/SRC/ztrevc.f
@@ -332,7 +332,7 @@
    90       CONTINUE
 *
 *           Solve the triangular system:
-*              (T(KI+1:N,KI+1:N) - T(KI,KI))'*X = SCALE*WORK.
+*              (T(KI+1:N,KI+1:N) - T(KI,KI))**H * X = SCALE*WORK.
 *
             DO 100 K = KI + 1, N
                T( K, K ) = T( K, K ) - T( KI, KI )
diff --git a/SRC/ztrsen.f b/SRC/ztrsen.f
index 7050cd24..1400f141 100644
--- a/SRC/ztrsen.f
+++ b/SRC/ztrsen.f
@@ -119,16 +119,16 @@
 *  transformation Z to move them to the top left corner of T. In other
 *  words, the selected eigenvalues are the eigenvalues of T11 in:
 *
-*                Z'*T*Z = ( T11 T12 ) n1
+*          Z**H * T * Z = ( T11 T12 ) n1
 *                         (  0  T22 ) n2
 *                            n1  n2
 *
-*  where N = n1+n2 and Z' means the conjugate transpose of Z. The first
+*  where N = n1+n2. The first
 *  n1 columns of Z span the specified invariant subspace of T.
 *
 *  If T has been obtained from the Schur factorization of a matrix
-*  A = Q*T*Q', then the reordered Schur factorization of A is given by
-*  A = (Q*Z)*(Z'*T*Z)*(Q*Z)', and the first n1 columns of Q*Z span the
+*  A = Q*T*Q**H, then the reordered Schur factorization of A is given by
+*  A = (Q*Z)*(Z**H*T*Z)*(Q*Z)**H, and the first n1 columns of Q*Z span the
 *  corresponding invariant subspace of A.
 *
 *  The reciprocal condition number of the average of the eigenvalues of
@@ -331,7 +331,7 @@
      $                      IERR )
             ELSE
 *
-*              Solve T11'*R - R*T22' = scale*X.
+*              Solve T11**H*R - R*T22**H = scale*X.
 *
                CALL ZTRSYL( 'C', 'C', -1, N1, N2, T, LDT,
      $                      T( N1+1, N1+1 ), LDT, WORK, N1, SCALE,
diff --git a/SRC/ztrsna.f b/SRC/ztrsna.f
index 20a8e2f8..69ace750 100644
--- a/SRC/ztrsna.f
+++ b/SRC/ztrsna.f
@@ -124,10 +124,10 @@
 *  The reciprocal of the condition number of an eigenvalue lambda is
 *  defined as
 *
-*          S(lambda) = |v'*u| / (norm(u)*norm(v))
+*          S(lambda) = |v**H*u| / (norm(u)*norm(v))
 *
 *  where u and v are the right and left eigenvectors of T corresponding
-*  to lambda; v' denotes the conjugate transpose of v, and norm(u)
+*  to lambda; v**H denotes the conjugate transpose of v, and norm(u)
 *  denotes the Euclidean norm. These reciprocal condition numbers always
 *  lie between zero (very badly conditioned) and one (very well
 *  conditioned). If n = 1, S(lambda) is defined to be 1.
@@ -302,7 +302,7 @@
                WORK( I, I ) = WORK( I, I ) - WORK( 1, 1 )
    20       CONTINUE
 *
-*           Estimate a lower bound for the 1-norm of inv(C'). The 1st
+*           Estimate a lower bound for the 1-norm of inv(C**H). The 1st
 *           and (N+1)th columns of WORK are used to store work vectors.
 *
             SEP( KS ) = ZERO
@@ -315,7 +315,7 @@
             IF( KASE.NE.0 ) THEN
                IF( KASE.EQ.1 ) THEN
 *
-*                 Solve C'*x = scale*b
+*                 Solve C**H*x = scale*b
 *
                   CALL ZLATRS( 'Upper', 'Conjugate transpose',
      $                         'Nonunit', NORMIN, N-1, WORK( 2, 2 ),
diff --git a/SRC/ztrsyl.f b/SRC/ztrsyl.f
index baf619c0..4c32dba1 100644
--- a/SRC/ztrsyl.f
+++ b/SRC/ztrsyl.f
@@ -209,17 +209,17 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
 *
-*        Solve    A' *X + ISGN*X*B = scale*C.
+*        Solve    A**H *X + ISGN*X*B = scale*C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-left corner column by column by
 *
-*            A'(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
+*            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
 *
 *        Where
-*                   K-1                         L-1
-*          R(K,L) = SUM [A'(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
-*                   I=1                         J=1
+*                   K-1                           L-1
+*          R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
+*                   I=1                           J=1
 *
          DO 60 L = 1, N
             DO 50 K = 1, M
@@ -257,19 +257,19 @@
 *
       ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A'*X + ISGN*X*B' = C.
+*        Solve    A**H*X + ISGN*X*B**H = C.
 *
 *        The (K,L)th block of X is determined starting from
 *        upper-right corner column by column by
 *
-*            A'(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+*            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
 *
 *        Where
 *                    K-1
-*           R(K,L) = SUM [A'(I,K)*X(I,L)] +
+*           R(K,L) = SUM [A**H(I,K)*X(I,L)] +
 *                    I=1
 *                           N
-*                     ISGN*SUM [X(K,J)*B'(L,J)].
+*                     ISGN*SUM [X(K,J)*B**H(L,J)].
 *                          J=L+1
 *
          DO 90 L = N, 1, -1
@@ -309,16 +309,16 @@
 *
       ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
 *
-*        Solve    A*X + ISGN*X*B' = C.
+*        Solve    A*X + ISGN*X*B**H = C.
 *
 *        The (K,L)th block of X is determined starting from
 *        bottom-left corner column by column by
 *
-*           A(K,K)*X(K,L) + ISGN*X(K,L)*B'(L,L) = C(K,L) - R(K,L)
+*           A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
 *
 *        Where
 *                    M                          N
-*          R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B'(L,J)]
+*          R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
 *                  I=K+1                      J=L+1
 *
          DO 120 L = N, 1, -1
diff --git a/SRC/ztzrqf.f b/SRC/ztzrqf.f
index ab172d69..1b1a1bd0 100644
--- a/SRC/ztzrqf.f
+++ b/SRC/ztzrqf.f
@@ -66,9 +66,9 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
-*                                                 (   0    )
-*                                                 ( z( k ) )
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
+*                                                   (   0    )
+*                                                   ( z( k ) )
 *
 *  tau is a scalar and z( k ) is an ( n - m ) element vector.
 *  tau and z( k ) are chosen to annihilate the elements of the kth row
@@ -142,7 +142,7 @@
 *
             IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
 *
-*              We now perform the operation  A := A*P( k )'.
+*              We now perform the operation  A := A*P( k )**H.
 *
 *              Use the first ( k - 1 ) elements of TAU to store  a( k ),
 *              where  a( k ) consists of the first ( k - 1 ) elements of
@@ -157,7 +157,7 @@
      $                     LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
 *
 *              Now form  a( k ) := a( k ) - conjg(tau)*w
-*              and       B      := B      - conjg(tau)*w*z( k )'.
+*              and       B      := B      - conjg(tau)*w*z( k )**H.
 *
                CALL ZAXPY( K-1, -DCONJG( TAU( K ) ), TAU, 1, A( 1, K ),
      $                     1 )
diff --git a/SRC/ztzrzf.f b/SRC/ztzrzf.f
index 47746b1d..b5d916e7 100644
--- a/SRC/ztzrzf.f
+++ b/SRC/ztzrzf.f
@@ -81,7 +81,7 @@
 *
 *  where
 *
-*     T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
+*     T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
 *                                                 (   0    )
 *                                                 ( z( k ) )
 *
diff --git a/SRC/zungl2.f b/SRC/zungl2.f
index fe45abf6..f636d7d1 100644
--- a/SRC/zungl2.f
+++ b/SRC/zungl2.f
@@ -19,7 +19,7 @@
 *  which is defined as the first m rows of a product of k elementary
 *  reflectors of order n
 *
-*        Q  =  H(k)' . . . H(2)' H(1)'
+*        Q  =  H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by ZGELQF.
 *
@@ -110,7 +110,7 @@
 *
       DO 40 I = K, 1, -1
 *
-*        Apply H(i)' to A(i:m,i:n) from the right
+*        Apply H(i)**H to A(i:m,i:n) from the right
 *
          IF( I.LT.N ) THEN
             CALL ZLACGV( N-I, A( I, I+1 ), LDA )
diff --git a/SRC/zunglq.f b/SRC/zunglq.f
index fa8edfe3..61992586 100644
--- a/SRC/zunglq.f
+++ b/SRC/zunglq.f
@@ -19,7 +19,7 @@
 *  which is defined as the first M rows of a product of K elementary
 *  reflectors of order N
 *
-*        Q  =  H(k)' . . . H(2)' H(1)'
+*        Q  =  H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by ZGELQF.
 *
@@ -185,7 +185,7 @@
                CALL ZLARFT( 'Forward', 'Rowwise', N-I+1, IB, A( I, I ),
      $                      LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(i+ib:m,i:n) from the right
+*              Apply H**H to A(i+ib:m,i:n) from the right
 *
                CALL ZLARFB( 'Right', 'Conjugate transpose', 'Forward',
      $                      'Rowwise', M-I-IB+1, N-I+1, IB, A( I, I ),
@@ -193,7 +193,7 @@
      $                      WORK( IB+1 ), LDWORK )
             END IF
 *
-*           Apply H' to columns i:n of current block
+*           Apply H**H to columns i:n of current block
 *
             CALL ZUNGL2( IB, N-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
      $                   IINFO )
diff --git a/SRC/zungr2.f b/SRC/zungr2.f
index 701d30f1..5fe697c8 100644
--- a/SRC/zungr2.f
+++ b/SRC/zungr2.f
@@ -19,7 +19,7 @@
 *  which is defined as the last m rows of a product of k elementary
 *  reflectors of order n
 *
-*        Q  =  H(1)' H(2)' . . . H(k)'
+*        Q  =  H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by ZGERQF.
 *
@@ -112,7 +112,7 @@
       DO 40 I = 1, K
          II = M - K + I
 *
-*        Apply H(i)' to A(1:m-k+i,1:n-k+i) from the right
+*        Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
 *
          CALL ZLACGV( N-M+II-1, A( II, 1 ), LDA )
          A( II, N-M+II ) = ONE
diff --git a/SRC/zungrq.f b/SRC/zungrq.f
index ef1d8326..ecd13396 100644
--- a/SRC/zungrq.f
+++ b/SRC/zungrq.f
@@ -19,7 +19,7 @@
 *  which is defined as the last M rows of a product of K elementary
 *  reflectors of order N
 *
-*        Q  =  H(1)' H(2)' . . . H(k)'
+*        Q  =  H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by ZGERQF.
 *
@@ -193,7 +193,7 @@
                CALL ZLARFT( 'Backward', 'Rowwise', N-K+I+IB-1, IB,
      $                      A( II, 1 ), LDA, TAU( I ), WORK, LDWORK )
 *
-*              Apply H' to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
+*              Apply H**H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right
 *
                CALL ZLARFB( 'Right', 'Conjugate transpose', 'Backward',
      $                      'Rowwise', II-1, N-K+I+IB-1, IB, A( II, 1 ),
@@ -201,7 +201,7 @@
      $                      LDWORK )
             END IF
 *
-*           Apply H' to columns 1:n-k+i+ib-1 of current block
+*           Apply H**H to columns 1:n-k+i+ib-1 of current block
 *
             CALL ZUNGR2( IB, N-K+I+IB-1, IB, A( II, 1 ), LDA, TAU( I ),
      $                   WORK, IINFO )
diff --git a/SRC/zunm2l.f b/SRC/zunm2l.f
index f2aa1f2a..e683ce00 100644
--- a/SRC/zunm2l.f
+++ b/SRC/zunm2l.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -168,17 +168,17 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(1:m-k+i,1:n)
+*           H(i) or H(i)**H is applied to C(1:m-k+i,1:n)
 *
             MI = M - K + I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,1:n-k+i)
+*           H(i) or H(i)**H is applied to C(1:m,1:n-k+i)
 *
             NI = N - K + I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/zunm2r.f b/SRC/zunm2r.f
index 6cf5779d..03322a2d 100644
--- a/SRC/zunm2r.f
+++ b/SRC/zunm2r.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -170,19 +170,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/zunml2.f b/SRC/zunml2.f
index 2397898d..a51dec3b 100644
--- a/SRC/zunml2.f
+++ b/SRC/zunml2.f
@@ -21,16 +21,16 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(k)' . . . H(2)' H(1)'
+*        Q = H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n
 *  if SIDE = 'R'.
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -170,19 +170,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = DCONJG( TAU( I ) )
diff --git a/SRC/zunmlq.f b/SRC/zunmlq.f
index ee8dc3bc..b6a5d3d4 100644
--- a/SRC/zunmlq.f
+++ b/SRC/zunmlq.f
@@ -26,7 +26,7 @@
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(k)' . . . H(2)' H(1)'
+*        Q = H(k)**H . . . H(2)**H H(1)**H
 *
 *  as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N
 *  if SIDE = 'R'.
@@ -241,19 +241,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL ZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB,
      $                   A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK,
diff --git a/SRC/zunmql.f b/SRC/zunmql.f
index ba08aa08..fece8c9b 100644
--- a/SRC/zunmql.f
+++ b/SRC/zunmql.f
@@ -237,17 +237,17 @@
      $                   A( 1, I ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**H is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**H is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL ZLARFB( SIDE, TRANS, 'Backward', 'Columnwise', MI, NI,
      $                   IB, A( 1, I ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/zunmqr.f b/SRC/zunmqr.f
index 19d236ac..c1bbe77e 100644
--- a/SRC/zunmqr.f
+++ b/SRC/zunmqr.f
@@ -234,19 +234,19 @@
      $                   LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL ZLARFB( SIDE, TRANS, 'Forward', 'Columnwise', MI, NI,
      $                   IB, A( I, I ), LDA, T, LDT, C( IC, JC ), LDC,
diff --git a/SRC/zunmr2.f b/SRC/zunmr2.f
index a4191b51..d341b399 100644
--- a/SRC/zunmr2.f
+++ b/SRC/zunmr2.f
@@ -21,16 +21,16 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(1)' H(2)' . . . H(k)'
+*        Q = H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by ZGERQF. Q is of order m if SIDE = 'L' and of order n
 *  if SIDE = 'R'.
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -75,7 +75,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -168,17 +168,17 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(1:m-k+i,1:n)
+*           H(i) or H(i)**H is applied to C(1:m-k+i,1:n)
 *
             MI = M - K + I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,1:n-k+i)
+*           H(i) or H(i)**H is applied to C(1:m,1:n-k+i)
 *
             NI = N - K + I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = DCONJG( TAU( I ) )
diff --git a/SRC/zunmr3.f b/SRC/zunmr3.f
index 7f879b2f..335b725c 100644
--- a/SRC/zunmr3.f
+++ b/SRC/zunmr3.f
@@ -21,11 +21,11 @@
 *
 *        Q * C  if SIDE = 'L' and TRANS = 'N', or
 *
-*        Q'* C  if SIDE = 'L' and TRANS = 'C', or
+*        Q**H* C  if SIDE = 'L' and TRANS = 'C', or
 *
 *        C * Q  if SIDE = 'R' and TRANS = 'N', or
 *
-*        C * Q' if SIDE = 'R' and TRANS = 'C',
+*        C * Q**H if SIDE = 'R' and TRANS = 'C',
 *
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
@@ -39,12 +39,12 @@
 *  =========
 *
 *  SIDE    (input) CHARACTER*1
-*          = 'L': apply Q or Q' from the Left
-*          = 'R': apply Q or Q' from the Right
+*          = 'L': apply Q or Q**H from the Left
+*          = 'R': apply Q or Q**H from the Right
 *
 *  TRANS   (input) CHARACTER*1
 *          = 'N': apply Q  (No transpose)
-*          = 'C': apply Q' (Conjugate transpose)
+*          = 'C': apply Q**H (Conjugate transpose)
 *
 *  M       (input) INTEGER
 *          The number of rows of the matrix C. M >= 0.
@@ -80,7 +80,7 @@
 *
 *  C       (input/output) COMPLEX*16 array, dimension (LDC,N)
 *          On entry, the m-by-n matrix C.
-*          On exit, C is overwritten by Q*C or Q'*C or C*Q' or C*Q.
+*          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
 *
 *  LDC     (input) INTEGER
 *          The leading dimension of the array C. LDC >= max(1,M).
@@ -182,19 +182,19 @@
       DO 10 I = I1, I2, I3
          IF( LEFT ) THEN
 *
-*           H(i) or H(i)' is applied to C(i:m,1:n)
+*           H(i) or H(i)**H is applied to C(i:m,1:n)
 *
             MI = M - I + 1
             IC = I
          ELSE
 *
-*           H(i) or H(i)' is applied to C(1:m,i:n)
+*           H(i) or H(i)**H is applied to C(1:m,i:n)
 *
             NI = N - I + 1
             JC = I
          END IF
 *
-*        Apply H(i) or H(i)'
+*        Apply H(i) or H(i)**H
 *
          IF( NOTRAN ) THEN
             TAUI = TAU( I )
diff --git a/SRC/zunmrq.f b/SRC/zunmrq.f
index 507c5596..d16a9d59 100644
--- a/SRC/zunmrq.f
+++ b/SRC/zunmrq.f
@@ -26,7 +26,7 @@
 *  where Q is a complex unitary matrix defined as the product of k
 *  elementary reflectors
 *
-*        Q = H(1)' H(2)' . . . H(k)'
+*        Q = H(1)**H H(2)**H . . . H(k)**H
 *
 *  as returned by ZGERQF. Q is of order M if SIDE = 'L' and of order N
 *  if SIDE = 'R'.
@@ -244,17 +244,17 @@
      $                   A( I, 1 ), LDA, TAU( I ), T, LDT )
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(1:m-k+i+ib-1,1:n)
+*              H or H**H is applied to C(1:m-k+i+ib-1,1:n)
 *
                MI = M - K + I + IB - 1
             ELSE
 *
-*              H or H' is applied to C(1:m,1:n-k+i+ib-1)
+*              H or H**H is applied to C(1:m,1:n-k+i+ib-1)
 *
                NI = N - K + I + IB - 1
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL ZLARFB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, A( I, 1 ), LDA, T, LDT, C, LDC, WORK,
diff --git a/SRC/zunmrz.f b/SRC/zunmrz.f
index f1dc10a2..53f0a8ec 100644
--- a/SRC/zunmrz.f
+++ b/SRC/zunmrz.f
@@ -268,19 +268,19 @@
 *
             IF( LEFT ) THEN
 *
-*              H or H' is applied to C(i:m,1:n)
+*              H or H**H is applied to C(i:m,1:n)
 *
                MI = M - I + 1
                IC = I
             ELSE
 *
-*              H or H' is applied to C(1:m,i:n)
+*              H or H**H is applied to C(1:m,i:n)
 *
                NI = N - I + 1
                JC = I
             END IF
 *
-*           Apply H or H'
+*           Apply H or H**H
 *
             CALL ZLARZB( SIDE, TRANST, 'Backward', 'Rowwise', MI, NI,
      $                   IB, L, A( I, JA ), LDA, T, LDT, C( IC, JC ),
diff --git a/SRC/zupmtr.f b/SRC/zupmtr.f
index 579ccae1..3b5bffe6 100644
--- a/SRC/zupmtr.f
+++ b/SRC/zupmtr.f
@@ -170,17 +170,17 @@
          DO 10 I = I1, I2, I3
             IF( LEFT ) THEN
 *
-*              H(i) or H(i)' is applied to C(1:i,1:n)
+*              H(i) or H(i)**H is applied to C(1:i,1:n)
 *
                MI = I
             ELSE
 *
-*              H(i) or H(i)' is applied to C(1:m,1:i)
+*              H(i) or H(i)**H is applied to C(1:m,1:i)
 *
                NI = I
             END IF
 *
-*           Apply H(i) or H(i)'
+*           Apply H(i) or H(i)**H
 *
             IF( NOTRAN ) THEN
                TAUI = TAU( I )
@@ -231,19 +231,19 @@
             AP( II ) = ONE
             IF( LEFT ) THEN
 *
-*              H(i) or H(i)' is applied to C(i+1:m,1:n)
+*              H(i) or H(i)**H is applied to C(i+1:m,1:n)
 *
                MI = M - I
                IC = I + 1
             ELSE
 *
-*              H(i) or H(i)' is applied to C(1:m,i+1:n)
+*              H(i) or H(i)**H is applied to C(1:m,i+1:n)
 *
                NI = N - I
                JC = I + 1
             END IF
 *
-*           Apply H(i) or H(i)'
+*           Apply H(i) or H(i)**H
 *
             IF( NOTRAN ) THEN
                TAUI = TAU( I )