Representations and norm estimations for the Moore–Penrose inverse of multiplicative perturbations of matrices.

A multiplicative perturbation of a matrixhas the formwithand, which can be expressed alternatively as, whereis the Moore–Penrose inverse ofT,andare introduced as In view of the aboveand, a new type of multiplicative perturbation called weak perturbation is introduced. A formula foris derived in the general case thatis a weak perturbation ofT. Based on this formula, an upper bound foris derived. The sharpness of the obtained upper bound is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]