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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 11, Pages 1779–1785
DOI: https://doi.org/10.31857/S0044466921110089 (Mi zvmmf11313) 		 
General numerical methods

On the set of matrices having $J_n(1)$ as the cosquare

Kh. D. Ikramov

Moscow Lomonosov State University, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466921110089
Abstract: Complex matrices having $J_n(1)$ as the cosquare are shown to be nonsingular matrices $X$ with the algebraic form $X=Y+iZ$, where the real matrices $Y$ and $Z$ are solutions to the matrix equation $(J_n(1)^{\mathrm{T}}W-W(J_n(1))^{-1}=0$. The form of such matrices $Y$ and $Z$ is described.
Key words: congruence, cosquare, Stein matrix equation, Sylvester matrix equation, elementary divisor.
Received: 21.02.2020
Revised: 21.02.2020
Accepted: 07.07.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 11, Pages 1743–1749
DOI: https://doi.org/10.1134/S0965542521110087
Bibliographic databases:
Document Type: Article
UDC: 519.61
Language: Russian
Citation: Kh. D. Ikramov, “On the set of matrices having $J_n(1)$ as the cosquare”, Zh. Vychisl. Mat. Mat. Fiz., 61:11 (2021), 1779–1785; Comput. Math. Math. Phys., 61:11 (2021), 1743–1749
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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