Representations for the Drazin Inverse of a 2 x 2 Block Matrix

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

“…, when the generalized Schur complement is equal to zero, which can be regarded as the generalizations of some results given in [5,20]. Finally, in section 5, we give a numerical example to illustrate our result of block matrix.…”

“…The importance of the Drazin inverse and its applications to singular differential equations and difference equations, to Morkov chains and iterative methods, to cryptography, to numerical analysis, to structured matrices and to perturbation bounds for the relative eigenvalue problems can be found in [2,[3][4][5].…”

Perturbation of the generalized Drazin inverse

“…Additive perturbation results for the GD-inverse were investigated by many authors (see [5,7,8,12,13,16] …”

“…Introduction. The Drazin inverse of an operator or a matrix has various applications in singular differential equations and singular difference equations, Markov chains, and iterative methods (see [1,2,3,4,16,17,22,23,30]). In addition, the perturbation analysis of the Drazin inverse is important from the perspectives of both pure and computational mathematics (see [2]- [4], [6]- [7], [19]- [29]).…”

“…In addition, the perturbation analysis of the Drazin inverse is important from the perspectives of both pure and computational mathematics (see [2]- [4], [6]- [7], [19]- [29]). The perturbation results of the Drazin inverse of a closed linear operator can be applied to the solution of perturbed linear equations and to the asymptotic behavior of C 0 -semigroup of bounded linear operators [2,16].…”