[Octave-bug-tracker] [bug #44061] U and V result matrices from svds are not othogonal

[Rik]

Follow-up Comment #3, bug #44061 (project octave):

This may be related to interpretation, and maybe something Octave should be
doing better.  If you read the documentation for svds in Octave it does not
say that U or V will be orthonormal matrices such that


U*U' = 1
V*V' = 1.


The only thing it states is that


A_approx = U*S*V'


And this does in fact work with the example:


full (A)
ans =

  -1  -1   0   0
  -1   1   0   0
   1  -1   0   0
   1   1   0   0

[U, S, V] = svds (A)

 U*S*V' - A
ans =

   0   0   0   0
   0   0   0   0
   0   0   0   0
   0   0   0   0



Can someone with access to Matlab run the example matrix?  According to their
documentation they are supposed to output orthonormal U and V matrices.

This doesn't appear to be a problem with this particular matrix.  I tried svds
on several matrices created with rand() and U and V are never orthonormal.




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