Geodesic
Congruence of unitary matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 94-96

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C. R. Johnson and S. Furtado showed that if two unitary matrices are $*$-congruent, then they are unitarily similar. In this note, an analogous statement concerning another type of matrix congruence, namely, the T-congruence is proved. Additionally, the problem of checking the T-congruence of given matrices using only a finite number of arithmetic operations is discussed. 
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     title = {Congruence of unitary matrices},
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Kh. D. Ikramov. Congruence of unitary matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 94-96. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a5/