Representations and norm estimations for the Moore–Penrose inverse of multiplicative perturbations of matrices
Xiaobo Zhang, Xuxu Fang, Chuanning Song, Qingxiang Xu · Linear and Multilinear Algebra · 2016
A multiplicative perturbation of a matrix has the form with and , which can be expressed alternatively as , where is the Moore–Penrose inverse of T, and are introduced asIn view of the above and , a new type of multiplicative perturbation called weak perturbation is introduced. A formula for is derived in the general case that is a weak perturbation of T. Based on this formula, an upper bound for is derived. The sharpness of the obtained upper bound is illustrated by some numerical examples.