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..?