(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If two square matrices, A and B are unitarily equivalent then A = QBQ* for some unitary Q of the same size as A and B. Prove that A and B are unitarily equivalent if and only if they have the same singular values

2. Relevant equations

3. The attempt at a solution

I started from the definition of singular values:

Au = sigma v for singular vectors u and v

A*v = sigma u

substitution A with QBQ*,

QBQ*u = sigma v

(QBQ*)*v = QB*Q*v = sigma u

Can't see how this leads to proving that the sigmas of A and B are the same..?

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# Homework Help: Singular values of unitarily equivalent matrices

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