Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 175, Pages 19–26
DOI: https://doi.org/10.36535/0233-6723-2020-175-19-26 (Mi into573) 		 
Congruences and unitary congruences in matrix theory

Kh. D. Ikramov

Lomonosov Moscow State University
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DOI: https://doi.org/10.36535/0233-6723-2020-175-19-26
Abstract: 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, Youla form, rational algorithm.
Bibliographic databases:
Document Type: Article
UDC: 512.643
MSC: 15A21, 15B99
Language: Russian
Citation: Kh. D. Ikramov, “Congruences and unitary congruences in matrix theory”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 175, VINITI, Moscow, 2020, 19–26
Citation in format AMSBIB
\Bibitem{Ikr20}
\by Kh.~D.~Ikramov
\paper Congruences and unitary congruences in matrix theory
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 175
\pages 19--26
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into573}
\crossref{https://doi.org/10.36535/0233-6723-2020-175-19-26}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4150667}
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