Characterizations of matrices which eigenprojections at zero are equal to a fixed perturbation

摘要

In this paper we characterize matrices B such that their eigenprojection Bπ corresponding to the eigenvalue 0 is a fixed perturbation of the eigenprojection of the matrix A, i.e., Bπ=Aπ+S. From this result we derive upper bounds for ∥BD∥ and for ∥BD−AD∥ in terms of ∥S∥ and ∥AD(B−A)∥. The error estimate is applied to perturbed linear systems.