A note on the group inverse of some 2 × 2 block matrices over skew fields

摘要

Let K be a skew field and Km×n be the set of all m × n matrices over K. In this paper, we give the necessary and sufficient conditions to the existence and the representations of the group inverse for block matrix AX+YBAB0 under some conditions, where A, Y ∈ Km×n, X, B ∈ Kn×m.