Characterizations and perturbation analysis of a class of matrices related to core-EP inverses

Abstract

[EN] Let A, B is an element of C-nxn with ind(A) = k and ind(B) = s and let L-B = (BB)-B-2(sic). A new condition (C-s,C-*): R(A(k)) boolean AND N((B-s)*) = {0} and R(B-s) boolean AND N((A(k))*) = {0}, is defined. Some new characterizations related to core-EP inverses are obtained when B satisfies condition (C-s,C-*). Explicit expressions of B(sic) and BB(sic) are also given. In addition, equivalent conditions, which guarantee that B satisfies condition (C-s,C-*), are investigated. We proved that B satisfies condition (C-s,C-*) if and only if L-B has a fixed matrix form. As an application, upper bounds for the errors parallel to B(sic) - A(sic)parallel to/parallel to A(sic)parallel to and parallel to BB(sic) - AA(sic)parallel to are studied. (c) 2021 Elsevier B.V. All rights reserved.