MATLAB SVD with Matlab

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],
[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?
 

Want to reply to this thread?

"SVD with Matlab" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top