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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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An algorithm for arbitrary matrices is given by Heydar Radjavi in 1962 (On unitary equivalence of arbitrary matrices, TAMS). The "arbitrary" in the title is there because the problem is trivial for normal matrices (you diagonalize both matrices, and check that the diagonalizations are the same up to order).

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  • $\begingroup$ Any recent significant development? $\endgroup$ – Dutta Jul 1 '15 at 17:47
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    $\begingroup$ Why? What's wrong with the 1962 method? $\endgroup$ – Igor Rivin Jul 1 '15 at 18:28
  • $\begingroup$ I read it completely. Thank you very much. $\endgroup$ – Dutta Jul 2 '15 at 9:06

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