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Here's my feeble attempt:

A = A* is the condition for a Hermitian matrix. So I try expanding both sides in terms of their SVD:

A = USV* and A* = (USV*)* = ... = VSU*

So equating I get:

VSU* = USV*

Now maybe through this I can conclude something about how V and U relate to each other but I don't know how...

Thanks for any help.

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    It will help to conclude that $U=V$. What happens if you multiply $VSU^*$ by $USV^*$? Note that order will matter, so consider both.2012-11-07

3 Answers 3