Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – Application of perturbation theory for simple invariant subspaces

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…”

Some results on the generalized Drazin inverse of operator matrices

“…The GD-inverse of the operator matrix has various applications in singular differential equations and singular difference equations, Markov chains and iterative methods [2,3,5,6,8,9,[11][12][13]15,16,18,23,25,27,30] and [38][39][40]. We introduce briefly an application of *Corresponding author.…”

Explicit formulae for the generalized drazin inverse of block matrices over a Banach algebra

“…The generalized Drazin inverse of block matrices have various applications in singular differential equations and singular difference equations, Markov chains and iterative methods, and so on. We refer the reader to see [10,27,29,34,35].…”