Geodesic
Congruence of unitary matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 94-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] C. R. Johnson, S. Furtado, “A generalization of Sylvester's law of inertia”, Linear Algebra Appl., 338 (2001), 287–290 | DOI | MR | Zbl

[2] R. A. Horn, C. R. Johnson, Matrix Analysis, Second Edition, Cambridge University Press, 2013 | MR | Zbl

[3] D. K. Faddeev, V. N. Faddeeva, Vychislitelnye metody lineinoi algebry, Fizmatgiz, M., 1963 | MR