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[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?