Additive perturbation results for the Drazin inverse

In this paper some new additive results for the Drazin inverse are presented. We give a formula for the Drazin inverse of a sum of two matrices under conditions on the matrices less restrictive than those imposed in the corresponding theorem given by Hartwig et al. (Linear Algebra Appl. 322 (2001) 207-217). We consider some aplications of our results to the perturbation of the Drazin inverse and analyze a number of special cases.