Group inverse for a class 2×2 block matrices over skew fields

摘要

Suppose K is a skew field. Let Kn×n denote the set of all matrices over K. For A∈Kn×n, the matrix X∈Kn×n is said to be the group inverse of A, if it holds that AXA=A,XAX=X,AX=XA. In this paper, we give the existence and the representation of the group inverse for block matrix M=AAB0(A,B∈Kn×n,A2=A) over skew fields, and give the existences and the representations of the group inverse for other block matrices.