Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

DOI10.1142/S1005386709000297zbMath1176.15020MaRDI QIDQ3633827

Qing-Wen Wang, Xin Liu, Guang-Jing Song

Publication date: 23 June 2009

Published in: Algebra Colloquium (Search for Journal in Brave)

zbMATH Keywords

generalized inversesdivision ringminimal rankmaximal ranksystem of matrix equations

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

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Cites Work

• The matrix equations \(AX=C\), \(XB=D\)
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• On the matrix equation \(AX=B\) with applications to the generators of a controllability matrix
• A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity
• Upper and lower bounds for ranks of matrix expressions using generalized inverses
• \(P\)-(skew)symmetric common solutions to a pair of quaternion matrix equations
• Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications
• Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
• The general solution to a system of real quaternion matrix equations
• A system of four matrix equations over von Neumann regular rings and its applications
• The solvability of two linear matrix equations
• Ranks of Solutions of the Matrix Equation AXB = C
• The Minimum Rank of a 3 × 3 Partial Block Matrix

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