PERTURBATION BOUNDS FOR g-INVERSES WITH RESPECT TO THE UNITARILY INVARIANT NORM

Let complex matrices A and B have the same sizes. Using the singular value decomposition, we characterize the g-inverse B(1) of B such that the distance between a given g-inverse of A and the set of all g-inverses of the matrix B reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed g-inverse. These results generalize and improve the existing results published recently to some extent.