On perturbation bounds of generalized core inverses of matrices
Yuefeng Gao, Baofeng Wu · Linear and Multilinear Algebra · 2023
This paper provides additive perturbation bounds for the generalized core inverse Ad,† of a complex matrix A. Given perturbation matrix E, we first present upper bounds for ‖(A+E)d,†−Ad,†‖2‖Ad,†‖2 under the condition R(E)⊆R(Ak),N(AkA†)⊆N(E),wherek=ind(A), and then under the condition (A+E)(A+E)d,†=AAd,†. We then explore an integral formula for the generalized core inverse of a perturbed matrix associated with a semi-stable matrix. Furthermore, a perturbation bound for ‖(A+E)d,†−Ad,†‖F is obtained without conditions. Sufficient conditions for the continuity of the generalized core inverse can be obtained as a result. Finally, numerical examples are presented to illustrate the derived bounds.