Explicit representations of the Drazin inverse of block matrix and modified matrix

Generalized Drazin inverses of anti-triangular block matrices

“…where T 1 is invertible and T 2 is quasinilpotent (see [1][2][3][4][5][6][7][8][9][10][11][13][14][15]18,19,[21][22][23][24][25][26][27]). Throughout this paper, we denote M as…”

Block representations of the Drazin inverse of a bipartite matrix

“…Since then, special cases of this problem have been studied. Some recent papers containing representations for the Drazin inverse of such 2 × 2 block matrices are [3], [4], [6], [7], [8], [9], [11] and [12]; however the general problem remains open.…”

Representations for the Drazin inverse of bounded operators on Banach space

“…This problem was investigated in many papers (see [21], [27], [14], [22], [33], [26], [8], [12]). In this paper we give a representation for the Drazin inverse of a 2 × 2 bounded operator matrix.…”