On the Group Inverse for the Sum of Matrices

Abstract

Let K m×n denote the set of all m × n matrices over a skew field K. In this paper, we give a necessary and sufficient condition for the existence of the group inverse of P + Q and its representation under the condition PQ = 0, where P, Q ∈ K n×n . In addition, in view of the natural characters of block matrices, we give the existence and representation for the group inverse of P + Q and P + Q + R under some conditions, where P, Q, R ∈ K n×n . 2010 Mathematics subject classification: primary 15A09.