A cancellation property of the Moore-Penrose inverse of triple products

Abstract

We study the matrix equation C(BXC) † B = X †, where X† denotes the Moore-Penrose inverse. We derive conditions for the consistency of the equation and express all its solutions using singular vectors of B and C. Applications to compliance matrices in molecular dynamics, to mixed reverse-order laws of generalized inverses and to weighted Moore-Penrose inverses are given. © 2009 Australian Mathematical Society.