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).
answered Jul 1, 2015 at 17:13
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$\begingroup$ Any recent significant development? $\endgroup$– SupriyoCommented Jul 1, 2015 at 17:47
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2$\begingroup$ Why? What's wrong with the 1962 method? $\endgroup$ Commented Jul 1, 2015 at 18:28
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$\begingroup$ I read it completely. Thank you very much. $\endgroup$– SupriyoCommented Jul 2, 2015 at 9:06