Error bounds for the perturbation of the Drazin inverse under some geometrical conditions

This paper studies the Drazin inverse for perturbed matrices. For that, given a square matrix A, we consider and characterize the class of matrices B with index s such that , and , where and denote the null space and the range space of a matrix A, respectively, and A^D denote the Drazin inverse of A. Then, we provide explicit representations for B^D and BB^D, and upper bounds for the relative error B^D-A^D/A^D and the error BB^D-AA^D. A numerical example illustrates that the obtained bounds are better than others given in the literature.