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Acta Mathematica Sinica

, Volume 21, Issue 2, pp 323–334 | Cite as

A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications

  • Qing Wen Wang
ORIGINAL ARTICLES

Abstract

We consider the system of four linear matrix equations A 1 X = C 1, XB 2 = C 2, A 3 XB 3 = C 3 and A 4 XB 4 = C 4 over ℛ, an arbitrary von Neumann regular ring with identity. A necessary and sufficient condition for the existence and the expression of the general solution to the system are derived. As applications, necessary and sufficient conditions are given for the system of matrix equations A 1 X = C 1 and A 3 X = C 3 to have a bisymmetric solution, the system of matrix equations A 1 X = C 1 and A 3 XB 3 = C 3 to have a perselfconjugate solution over ℛ with an involution and char ℛ ≠2, respectively. The representations of such solutions are also presented. Moreover, some auxiliary results on other systems over ℛ are obtained. The previous known results on some systems of matrix equations are special cases of the new results.

Keywords

von Neumann regular ring System of matrix equations Perselfconjugate matrix Centrosymmetric matrix Bisymmetric matrix 

MR (2000) Subject Classification

15A06 15A24 15A33 15A57 15A09 16E50 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghai 200444P. R. China

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