Perturbation of the generalized Drazin inverse

Abstract

Abstract. In this paper, we investigate the perturbation of the generalized Drazin invertible matrices and derive explicit generalized Drazin inverse expressions for the perturbations under certain restrictions on the perturbing matrices.

Perturbation bound for the generalized Drazin inverse of an operator in Banach space

“…Xu et al considered the stable perturbation of the Drazin inverse of the square matrices in [30]. In [10], Deng and Wei considered the perturbation for the generalized Drazin inverse of a bounded linear operator. They also gave an explicit generalized Drazin inverse expression for the perturbation under certain restrictions on the perturbing matrices.…”

“…The motivation of the results in this paper is from those given in [10], which is considered the perturbation of the GD inverse in the following cases:…”