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Let two real matrices $A$ and $B$ are unitarybe unitarily equivalent. How to determine (computationally or theoriticallytheoretically) the unitary operator $U$ s.t. $A = UBU^\dagger$? Is it possible for some special class of matrices? Please give me some references.

Let two real matrices $A$ and $B$ are unitary equivalent. How to determine (computationally or theoritically) the unitary operator $U$ s.t. $A = UBU^\dagger$? Is it possible for some special class of matrices? Please give me some references.

Let two real matrices $A$ and $B$ be unitarily equivalent. How to determine (computationally or theoretically) the unitary operator $U$ s.t. $A = UBU^\dagger$? Is it possible for some special class of matrices? Please give me some references.

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How to determine an unitary operator involved in an unitary transformation?

Let two real matrices $A$ and $B$ are unitary equivalent. How to determine (computationally or theoritically) the unitary operator $U$ s.t. $A = UBU^\dagger$? Is it possible for some special class of matrices? Please give me some references.