On the perturbation bounds of g-inverses and oblique projections

Let A{1} and be two sets of g-inverses of matrices A and , respectively. For any A-∈A{1}, we deduce general formulas of g-inverse , such that the distances between the two g-inverses or oblique projections are the smallest under appropriated norms, and obtain the corresponding distances. With these results, we derive perturbation bounds of the nearest perturbed g-inverses, oblique projections, and consistent linear equations under rank preserving condition . Numerical examples are also provided to verify our analysis.