一类反三角矩阵的群逆和Drazin逆

doi:10.16088/j.issn.1001-6600.2015.03.009

Journal of Guangxi Normal University(Natural Science Edition) ›› 2015, Vol. 33 ›› Issue (3): 61-65.doi: 10.16088/j.issn.1001-6600.2015.03.009

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The Group Inverses and Drazin Inverses of a Class of Anti-triangular Block Matrices

LIU Xi-fu

School of Science, East China Jiaotong University, Nanchang Jiangxi 330013, China

Received:2015-01-09 Online:2015-05-10 Published:2018-09-20

Abstract

Abstract: The research on the group inverse and Drazin inverse of the anti-triangular block matrix M=PQI0 was always done under some conditions for the sub-matrices. In this paper, some results are obtained under some new conditions, namely, when P is nonsingular or ind(Q)≤1, sufficient and necessary conditions for the existence of the group inverse of M are developed and the expressions of the group inverse of M are presented. Moreover, based on the above results, the representations for Drazin inverses of M are obtained under conditions ind(P)≤1, P^πQP=0 and ind(P^#QPP^#)≤1, or on the conditions PQQ^π=0 and Q²Q^D+Q^πPQ^π are nonsingular.

Key words: group inverse, Drazin inverse, anti-triangular block matrix

CLC Number:

O151.21

LIU Xi-fu. The Group Inverses and Drazin Inverses of a Class of Anti-triangular Block Matrices[J].Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(3): 61-65.

References

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