Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (3): 708-717.

• Articles • Previous Articles     Next Articles

The Weighted Generalized Inverses of Matrices over Rings

 LIAO Zu-Hua, HUANG Yu, YI Li-Hua   

  1. School of Science, Jiangnan University, Jiangsu Wuxi |214122
  • Received:2008-03-25 Revised:2009-06-25 Online:2010-05-25 Published:2010-05-25
  • Supported by:

    江南大学创新团队发展计划项目(200902)资助

Abstract:

In this paper, we give a new kind of answer from another aspect to an open problem posed by   Hartwig R E[27]. Let R be an arbitrary ring with involution *. We define a new type of the weighted generalized inverse of matrices over R, denoted by A+P, Q, and give the necessary and sufficient conditions for the existence of A+P, Q. And several expressions of A+P, Q are also given. Meanwhile, some important properties are obtained.

Key words: Ring, Matrices, Weighted generalized inverse, Epic-monic factorization

CLC Number: 

  • 15A09
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