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ELA

GROUP INVERSE FOR THE BLOCK MATRIX WITH

TWO IDENTICAL SUBBLOCKS OVER SKEW FIELDS

∗

JIEMEI ZHAO† AND CHANGJIANG BU§†‡

Abstract. LetK be a skew field andKn×n be the set of alln×nmatrices overK. The

purpose of this paper is to give some necessary and sufficient conditions for the existence and the representations of the group inverse of the block matrixAC

B D

under some conditions.

Key words. Skew fields, Block matrix, Group inverse.

AMS subject classifications.15A09; 65F20.

∗Received by the editors on June 2009. Accepted for publication on July 31, 2010 Handling

Editors: Roger A. Horn and Fuzhen Zhang.

†College of Automation, Harbin Engineering University, Harbin 150001, P. R. China.

([email protected]). Supported by the NSFH, No.159110120002.

‡Dept. of Applied Math., College of Science, Harbin Engineering University, Harbin 150001, P.

R. China.§Corresponding author. Email: [email protected]

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 21, pp. 63-75, October 2010

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