Some structures of submatrices in solution to the paire of matrix equations \(AX=C,XB=D\)

DOI10.3934/mfc.2022023zbMath1530.15009OpenAlexW4285169720MaRDI QIDQ6112830

Radja Belkhiri, Sihem Guerarra

Publication date: 7 August 2023

Published in: Mathematical Foundations of Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mfc.2022023

zbMATH Keywords

inertiamatrix equationMoore-Penrose generalized inverserank formulas

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Cites Work

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• Generalized reflexive and anti-reflexive solutions of \(AX=B\)
• The common \((P,Q)\) generalized reflexive and anti-reflexive solutions to \(AX=B\) and \(XC=D\)
• The \((P,Q)\)-(skew)symmetric extremal rank solutions to a system of quaternion matrix equations
• Maximization and minimization of the rank and inertia of the Hermitian matrix expression \(A-BX-(BX)^{*}\) with applications
• An expression of the general common least-squares solution to a pair of matrix equations with applications
• The matrix equations \(AX=C\), \(XB=D\)
• Equalities and inequalities for inertias of Hermitian matrices with applications
• Least-squares solutions to the matrix equations \(AX = B\) and \(XC = D\)
• Singular value and generalized singular value decompositions and the solution of linear matrix equations
• The matrix equations \(AX=B, XC=D\) with \(PX= sXP\) constraint
• The general solution to a system of real quaternion matrix equations
• On the Hermitian structures of the solution to a pair of matrix equations
• Matrix theory. Basic results and techniques

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