The Drazin Inverses of the Sum of Two Matrices and Block Matrix

Abstract

Abstract. In this paper, we give a formula of (P + Q) D under the conditions P 2 Q + QP Q = 0 and P 3 Q = 0. Then applying it to give some results) (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.

Some Results for the Drazin Inverses of the Sum of Two Matrices and Some Block Matrices

“…In 2011, Yang and Liu [11] established some expressions of ( + ) when 2 = 0 and = 0, and in 2012, Bu et al [12] got the explicit representation of ( + ) when 2 = 0, 2 = 0, 3 = 0, and = 0, 2 = 0, respectively. Other related results have been studied in [4,[13][14][15][16][17][18][19].…”