Displacement rank of the Drazin inverse

The Expression of the Drazin Inverse with Rank Constraints

Full-rank and Determinantal Representation of the Drazin Inverse

In this article we introduce a full-rank representation of the Drazin inverse AD of a given complex matrix A, which is based on an arbitrary full-rank decomposition of Al, l ≥ k, where k is the index of A. We show that the known representation of the Drazin inverse of A, devised in [7], represents a partial case of this result. Using this general representation, we introduce a determinantal rep...

Continuity of the Drazin Inverse

In this paper we investigate the continuity of the Drazin inverse of a bounded linear operator on Banach space. Then as a corollary, among other things, we get the well known result of Campbell and Meyer ([1]) for the continuity of the Drazin inverse of square matrix.

Rank Equalities for Moore-penrose Inverse and Drazin Inverse over Quaternion

In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or p...

Ela Perturbation of the Generalized Drazin Inverse

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.