Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero

Abstract

AbstractLet Aπ denote the eigenprojection of a matrix A corresponding to the eigenvalue 0. We characterize matrices B such that Bπ=Aπ, and derive from the results: (1) error bounds for the Drazin inverse of a perturbation, (2) improvement of error bounds given recently by Wei [10], Wei and Wang [11] and Castro González et al. [4], and (3) a new characterization of EP matrices