F08VSF Example Program Results Numerical rank of (A**T B**T)**T (K+L) 4 Upper triangular matrix S 1 2 1 ( -2.7118E+00, 0.0000E+00) ( -1.4390E+00, -1.0315E+00) 2 ( -1.8583E+00, 0.0000E+00) 3 4 3 4 1 ( -1.0543E-01, 1.3176E+00) ( -3.9240E-01, -1.9504E-01) 2 ( -9.4529E-01, 1.9279E-01) ( 1.4355E+00, 2.6313E-01) 3 ( 2.9079E+00, 0.0000E+00) ( -2.3946E-01, 1.8856E-01) 4 ( -1.5759E+00, 0.0000E+00) Upper triangular matrix T 1 2 1 ( 1.4142E+00, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 2 ( 1.4142E+00, 0.0000E+00) Orthogonal matrix U 1 2 1 ( -1.3038E-02, -3.2595E-01) ( -1.4039E-01, -2.6167E-01) 2 ( 4.2764E-01, -6.2582E-01) ( 8.6298E-02, -3.8174E-02) 3 ( -3.2595E-01, 1.6428E-01) ( 3.8163E-01, -1.8219E-01) 4 ( 1.5906E-01, -5.2151E-03) ( -2.8207E-01, 1.9732E-01) 5 ( -1.7210E-01, -1.3038E-02) ( -5.0942E-01, -5.0319E-01) 6 ( -2.6336E-01, -2.4772E-01) ( -1.0861E-01, 2.8474E-01) 3 4 1 ( 2.4357E-01, -7.7956E-01) ( -7.4007E-02, -2.7823E-01) 2 ( -3.2035E-01, 1.4475E-01) ( 1.0740E-01, 1.8824E-01) 3 ( 1.7217E-01, -1.4009E-03) ( -4.9770E-01, 1.7826E-01) 4 ( 2.5307E-01, 1.9053E-01) ( -3.7794E-01, 2.6816E-01) 5 ( 3.2057E-02, 1.8358E-01) ( 2.0422E-01, 1.6601E-01) 6 ( 1.4142E-01, -1.5707E-01) ( -8.7335E-02, 5.4683E-01) 5 6 1 ( -4.5947E-02, 1.4052E-04) ( -5.2773E-02, -2.2492E-01) 2 ( -8.0311E-02, -4.3605E-01) ( -3.8117E-02, -2.1907E-01) 3 ( 5.9714E-02, -5.8974E-01) ( -1.3850E-01, -9.0941E-02) 4 ( -4.6443E-02, 3.0864E-01) ( -3.7354E-01, -5.5148E-01) 5 ( 5.7843E-01, -1.2439E-01) ( -1.8815E-02, -5.5686E-02) 6 ( 1.5763E-02, 4.7130E-02) ( 6.5007E-01, 4.9173E-03) Orthogonal matrix V 1 2 1 ( 1.0000E+00, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 2 ( 0.0000E+00, 0.0000E+00) ( 1.0000E+00, 0.0000E+00) Orthogonal matrix Q 1 2 1 ( 7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 2 ( 0.0000E+00, 0.0000E+00) ( 7.0711E-01, 0.0000E+00) 3 ( 7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 4 ( 0.0000E+00, 0.0000E+00) ( 7.0711E-01, 0.0000E+00) 3 4 1 ( 7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 2 ( 0.0000E+00, 0.0000E+00) ( 7.0711E-01, 0.0000E+00) 3 ( -7.0711E-01, 0.0000E+00) ( 0.0000E+00, 0.0000E+00) 4 ( 0.0000E+00, 0.0000E+00) ( -7.0711E-01, 0.0000E+00)