Example description

 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)

 Unitary 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)

 Unitary 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)

 Unitary 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)