Abstract
In this paper, we study the multiplicative perturbation of an operator of the form , where X and Y are invertible. Based on this result, we study the Moore–Penrose invertibility of block matrix M with Schur complement having closed range. We recover the cases when a Schur complement in M is either equal to zero or nonsingular. The necessary and sufficient conditions for the existence as well as the expressions for the Moore–Penrose inverses are obtained.
Notes
No potential conflict of interest was reported by the authors.