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],(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

A = U\Sigma V^H, A^T=(U\Sigma V^H)^T

[/tex]

so that

[tex]

U\Sigma V^H=(V^H)^T\Sigma U^T.

[/tex]

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?

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# SVD with Matlab

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