Title

An Improvement on the Perturbation of the Group Inverse and Oblique Projection

Document Type

Article

Publication Date

11-15-2001

Publication Title

Linear Algebra and its Applications

DOI

10.1016/S0024-3795(01)00369-X

ISSN

0024-3795

Abstract

The perturbations of the group inverse A# and oblique projection AA# of a square matrix A have been previously studied. Under certain assumptions on the matrix A and a perturbation matrix E, upper bounds for ∥B#∥,∥BB#∥,∥B#−A#∥∥A#∥and∥BB#−AA#∥∥AA#∥, where B=A+E, are given in the literature. Recently, upper bounds for the general case have been published by Y. Wei [Appl. Math. Comp. 98 (1999) 29]. However, the special cases in the literature and the continuity of the group inverse do not follow from the general upper bounds. In this paper, we derive new general upper bounds which not only cover all the special cases but also are sharper than Wei's results such that the continuity of the group inverse directly follows. A numerical example is given to illustrate the sharpness of the new general upper bounds.

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