On perturbation bounds of generalized core inverses of matrices

AbstractThis 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.Keywords: Generalized core inverseperturbation boundcontinuityFrobenius normAMS Subject Classifications: 15A0965F3534D10 AcknowledgmentsThe authors are highly grateful to the editor and the anonymous referees for their valuable suggestions, which greatly improved the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis research is supported by the National Natural Science Foundation of China (No. 12001368), and sponsored by Shanghai Sailing Program (No. 20YF1433100).