Geodesic
Congruences and unitary congruences in matrix theory
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 19-26.

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This paper is a review of basic facts related to important matrix transformations such as congruence, pseudo-similarity, and unitary congruence. The concept of a rational algorithm is formulated and the question of which problems in the congruence theory can be solved by rational algorithms is discussed.
Keywords: $T$-congruence, $*$-congruence, similarity, pseudo-similarity, canonical form, co-square, Schur form
Mots-clés : Youla form, rational algorithm. 
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Kh. D. Ikramov. Congruences and unitary congruences in matrix theory. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 19-26. http://geodesic.mathdoc.fr/item/INTO_2020_175_a1/

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