SVD(M.transpose())

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Mr. Moler:


Msub =  r = 4 col = 5

     0.0933     0.0991     0.0438     0.0134     0.0004
     0.0263     0.0902     0.0812     0.0473     0.0049
     0.0049     0.0473     0.0812     0.0902     0.0263
     0.0004     0.0134     0.0438     0.0991     0.0933

Msub Transposed =  r = 5 col = 4

     0.0933     0.0263     0.0049     0.0004
     0.0991     0.0902     0.0473     0.0134
     0.0438     0.0812     0.0812     0.0438
     0.0134     0.0473     0.0902     0.0991
     0.0004     0.0049     0.0263     0.0933

U =  r = 5 col = 4

     0.2557     -0.4986     0.6181     -0.5014
     0.5356     -0.5014     -0.0512     0.4986
     0.5437     0.0000     -0.4803     -0.0000
     0.5356     0.5014     -0.0512     -0.4986
     0.2557     0.4986     0.6181     0.5014

S =  r = 4 col = 4

     0.2345     0.0000     0.0000     0.0000
     0.0000     0.1342     0.0000     0.0000
     0.0000     0.0000     0.0581     0.0000
     0.0000     0.0000     0.0000     0.0160

V =  r = 4 col = 4

     0.4606     -0.6652     0.5365     -0.2397
     0.5365     -0.2397     -0.4606     0.6652
     0.5365     0.2397     -0.4606     -0.6652
     0.4606     0.6652     0.5365     0.2397

Msub Transposed = U * S * V'

Msub = (U * S * V')' = V * S' * U'

rank(Msub) = 4 and U has 4 columns => null space of Msub is empty
which does not make sense
   
So in this case we cannot find the null space of Msub by svd(Msub.transpose())?

Thomas Pham