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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 9, Pages 1460–1466 (Mi zvmmf241)  
On special solutions to the matrix equations $X\bar X=I$ и $X\bar X=-I$

Kh. D. Ikramov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
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Abstract: The matrix equations $X\bar X=I$ and $X\bar X=-I$ are important in the theory of consimilarity. For the first equation, a characterization of solutions was given in Section 4.6 of Matrix Analysis by Horn and Johnson. Since this characterization is not constructive, a complete and constructive description of solutions to these equations is derived under one of the following assumptions: (a) $X$ is a normal matrix, or (b) $X$ is a conjugate-normal matrix.
Key words: similarity of matrices, consimilarity of matrices, unitary congruence, normal matrix, conjugate-normal matrix.
Received: 02.03.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 9, Pages 1402–1408
DOI: https://doi.org/10.1134/S0965542507090023
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
Citation: Kh. D. Ikramov, “On special solutions to the matrix equations $X\bar X=I$ и $X\bar X=-I$”, Zh. Vychisl. Mat. Mat. Fiz., 47:9 (2007), 1460–1466; Comput. Math. Math. Phys., 47:9 (2007), 1402–1408
Citation in format AMSBIB
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\pages 1460--1466
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