Group inverses for some 2 × 2 block matrices over rings

doi:10.1007/s11464-016-0490-6

Front. Math. China

2016, Vol. 11

Issue (3) : 521-538 https://doi.org/10.1007/s11464-016-0490-6

RESEARCH ARTICLE

Group inverses for some 2 × 2 block matrices over rings

Chongguang CAO,Yingchun WANG,Yuqiu SHENG(

)

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

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Abstract

We first consider the group inverses of the block matrices (A0BC) over a weakly finite ring. Then we study the sufficient and necessary conditions for the existence and the representations of the group inverses of the block matrices (ACBD) over a ring with unity 1 under the following conditions respectively: (i) B = C, D = 0, B^# and (B^πA)^# both exist; (ii) B is invertible and m = n; (iii) A^#and (D - CA^#B)^# both exist, C = CAA^#, where A and D are m × m and n × n matrices, respectively.

Keywords Group inverse block matrix right Ore domain associative ring

Corresponding Author(s): Yuqiu SHENG

Issue Date: 17 May 2016

Cite this article:

Chongguang CAO,Yingchun WANG,Yuqiu SHENG. Group inverses for some 2 × 2 block matrices over rings[J]. Front. Math. China, 2016, 11(3): 521-538.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0490-6
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I3/521

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