Multiplicative perturbations of matrices and the generalized triple reverse order law for the Moore-Penrose inverse

摘要

For a matrix A, let A(dagger) denote its Moore-Penrose inverse. A matrix M is called a multiplicative perturbation of T is an element of C-mxn if M = ET F* for some E is an element of C-mxm and F is an element of C-nxn. Based on the alternative expression for M as M = (ETT dagger).T.((FTT)-T-dagger)*, the generalized triple reverse order law for the Moore-Penrose inverse is obtained as