abs_vol21pp63-75. 27KB Jun 04 2011 12:05:49 AM

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 and}Kn×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.}

(zhao-jiemei500@163.com). Supported by the NSFH, No.159110120002.

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

R. China.§_{Corresponding author. Email: buchangjiang@hrbeu.edu.cn}

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