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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# SVD with Matlab

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**