F08VEF Example Program Results Numerical rank of (A**T B**T)**T (K+L) 3 Upper triangular matrix S 1 2 3 1 -2.0569E+00 1.0771E+01 -7.2814E+00 2 7.1947E+00 -7.5262E+00 3 5.8129E-01 Upper triangular matrix T 1 2 1 8.0623E+00 -3.1305E+00 2 -4.9193E+00 Orthogonal matrix U 1 2 3 4 1 -1.3484E-01 5.1025E-01 -2.4351E-01 8.1373E-01 2 6.7420E-01 -5.4670E-01 -3.5349E-01 3.4874E-01 3 2.6968E-01 4.8292E-01 -6.9127E-01 -4.6499E-01 4 6.7420E-01 4.5558E-01 5.8129E-01 1.5127E-15 Orthogonal matrix V 1 2 1 -4.4721E-01 8.9443E-01 2 8.9443E-01 4.4721E-01 Orthogonal matrix Q 1 2 3 1 -8.3205E-01 5.5470E-01 0.0000E+00 2 5.5470E-01 8.3205E-01 0.0000E+00 3 0.0000E+00 0.0000E+00 -1.0000E+00