Unitary Equivalence of Matrices
We define the class of unitarily equivalent matrices. This definition is the same as equivalent matrices, but the invertible assumption is replaced with a unitary assumption. We prove that two unitarily equivalent matrices have the same Frobenius norm. The converse of this result is only true with additional assumptions on traces of words in A and A^* and was proved by Specht. We give an example of two matrices which are similar but not unitarily equivalent.
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