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The Generalized Inverse A(2)T, S of a Matrix Over an Associative Ring

Part of: Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

Yaoming Yu  and
Guorong Wang
Yaoming Yu
Affiliation:
College of EducationShanghai Normal UniversityShanghai 200234People's Republic of Chinayuyaoming@online.sh.cn
Guorong Wang
Affiliation:
College of MathematicsScience Shanghai Normal UniversityShanghai 200234People's Republic of Chinagrwang@shnu.edu.cn
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Abstract

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In this paper we establish the definition of the generalized inverse A(2)T, S which is a {2} inverse of a matrix A with prescribed image T and kernel s over an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverse and some explicit expressions for of a matrix A over an associative ring, which reduce to the group inverse or {1} inverses. In addition, we show that for an arbitrary matrix A over an associative ring, the Drazin inverse Ad, the group inverse Ag and the Moore-Penrose inverse . if they exist, are all the generalized inverse A(2)T, S.

MSC classification

Secondary: 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 3 , December 2007 , pp. 423 - 438
Copyright
Copyright © Australian Mathematical Society 2007

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