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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 4, Pages 555–557
DOI: https://doi.org/10.7868/S0044466915040183 (Mi zvmmf10182) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Solvability conditions for the matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$

Yu. O. Vorontsov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Full-text PDF (163 kB) Citations (3)
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DOI: https://doi.org/10.7868/S0044466915040183
Abstract: Under certain restrictions on the matrix coefficients of the quadratic matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$, solvability conditions for this equation are given, and its relationship with an equation of the form $XAX=B$ is found. Certain specific types of matrix coefficients obeying the above solvability conditions are indicated.
Key words: quadratic matrix equation, symmetric matrix, square root of a matrix, solvability of a matrix equation.
Received: 17.04.2014
Revised: 11.11.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 4, Pages 546–548
DOI: https://doi.org/10.1134/S096554251504017X
Bibliographic databases:
Document Type: Article
UDC: 519.61
MSC: 15A24
Language: Russian
Citation: Yu. O. Vorontsov, “Solvability conditions for the matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$”, Zh. Vychisl. Mat. Mat. Fiz., 55:4 (2015), 555–557; Comput. Math. Math. Phys., 55:4 (2015), 546–548
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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