This article is cited 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

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.

UDC: 519.61

MSC: 15A24

Received: 17.04.2014
Revised: 11.11.2014

DOI: 10.7868/S0044466915040183

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:4, 546–548

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