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SVD with Matlab

  1. Oct 8, 2007 #1
    For a square, complex-symmetric matrix [tex]A[/tex], the columns of the right and left matrices [tex]U[/tex] and [tex]V[/tex] of the singular value decomposition should be complex conjugates, since for [tex]A=A^T, A\in{\mathbb C}^{N\times N}[/tex],
    A = U\Sigma V^H, A^T=(U\Sigma V^H)^T
    so that
    U\Sigma V^H=(V^H)^T\Sigma U^T.
    Then we have [tex]U=(V^H)^T[/tex], right? So why isn't this the case when I run a few experiments with Matlab? The magnitudes of the elements of [tex]U[/tex] and [tex]V[/tex] are equal, but they aren't conjugates. The expected relationship holds for real [tex]A[/tex], where [tex]U[/tex] and [tex]V[/tex] are real-valued, but not for complex symmetric matrices. Who's screwed up here, me or Matlab?
  2. jcsd
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