The perturbation bound for the T-Drazin inverse of tensor and its application

Abstract

In this paper, let A and B be n x n x p complex tensors and B = A + E. Denote the T-Drazin inverse of A by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering the solution of singular tensor equation A* x = b, (b ? R(AD)) at the same time. The optimal perturbation of T-Drazin inverse of tensors and the solution of a system of tensor equations have been given.