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ELA

SOME RESULTS ON GROUP INVERSES OF BLOCK MATRICES

OVER SKEW FIELDS

∗

CHANGJIANG BU†, JIEMEI ZHAO†, AND KUIZE ZHANG†

Abstract. In this paper, necessary and sufficient conditions are given for the existence of the group inverse of the block matrix A A

B 0

over any skew field, whereA, Bare both square and rank(B)≥rank(A). The representation of this group inverse and some relative additive results are also given.

Key words. Skew, Block matrix, Group inverse.

AMS subject classifications.15A09.

∗Received by the editors October 11, 2008. Accepted for publication February 20, 2009. Handling

Editor: Ravindra B. Bapat.

†Department of Applied Mathematics, College of Science, Harbin Engineering University, Harbin

150001, P. R. China ([email protected], [email protected], [email protected]). Supported by the Natural Science Foundation of Heilongjiang Province, No.159110120002.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 117-125, February 2009

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