An improvement on the perturbation of the group inverse and oblique projection Original Research Article

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 image 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 Weiʹs 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.