- #1

Codezion

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## Homework Statement

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

## Homework Equations

## 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..?