Filomat 2017 Volume 31, Issue 12, Pages: 3685-3692
https://doi.org/10.2298/FIL1712685Z
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A note on the group inverses of block matrices over rings
Zhang Hanyu (Group of Mathematical, Jidong second middle school, Jidong, PR China)
Suppose R is an associative ring with identity 1. 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 matrix (AX+YB B A 0)
and M = (A B C D) under some conditions. Some examples are given to
illustrate our results.
Keywords: ring, group inverse, block matrix, anti-triangular