Expression for the multiplicative perturbation of the Moore–Penrose inverse
Chunyuan Deng, Rufang Liu, Xiunan Wang · Linear and Multilinear Algebra · 2017
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.