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ELA

GROUP INVERSES FOR MATRICES OVER A BEZOUT DOMAIN

∗

CHONGGUANG CAO† AND JUYAN LI†

Abstract. SupposeRis a Bezout domain. In this paper, some necessary and sufficient con-ditions for the existence of the group inverse for square matrix overRare given, the conditions for the existence of the group inverse of products of matrices are studied, and the equivalent conditions for reverse order law of group inverse of product of matrices are obtained. Also the existence and the representation of the group inverse for a class 2×2 block matrices overRare studied, and some

well known relative results are generalized.

Key words. Bezout domain, Group inverse, RightR–module, Block matrix.

AMS subject classifications.15A09.

∗Received by the editors June 4, 2009. Accepted for publication September 25, 2009. Handling

Editor: Harm Bart.

†Department of Mathematics, Heilongjiang University, Harbin, 150080, P. R. China

([email protected], [email protected]). Supported by Nation Science Foundation of China, No. 10671026.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 600-612, October 2009

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