Geodesic
On matrices whose cosquares are diagonalizable and have real spectra
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 1, pp. 53-57 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that the algorithm for verifying congruence of square roots of Hermitian matrices proposed earlier by the author can be extended to the considerably more broad class of matrices whose cosquares are diagonalizable and have real spectra. 
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     title = {On matrices whose cosquares are diagonalizable and have real spectra},
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Kh. D. Ikramov. On matrices whose cosquares are diagonalizable and have real spectra. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 1, pp. 53-57. http://geodesic.mathdoc.fr/item/SJVM_2022_25_1_a3/

[1] Kh.D. Ikramov, “Square roots of hermitian matrices and a rational algorithm for checking their congruence”, Moscow University Computational Mathematics and Cybernetics, 43:3 (2019), 95–100 | DOI | MR | Zbl

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