Geodesic
A criterion for unitary congruence between complex matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 9-19 
Yu. A. Al'pin; Kh. D. Ikramov. A criterion for unitary congruence between complex matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIV, Tome 395 (2011), pp. 9-19. http://geodesic.mathdoc.fr/item/ZNSL_2011_395_a1/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $A$ and $B$ be square complex matrices. Based on an important result of Y. P. Hong and R. A. Horn, we propose a criterion for verifying unitary congruence of these matrices. The criterion requires that a finite number of arithmetic operations be performed. No criteria with this finiteness property were previously known.

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