The Perturbation Bound for the T-Drazin Inverse of Tensor and its Application

In this paper, let A and B be n x n x p complex tensors and B = A + epsilon. Denote the T-Drazin inverse of A by A(D). We give a perturbation bound for parallel to B-D -A(D)parallel to/parallel to A(D)parallel to under condition (W). Considering the solution of singular tensor equation A* x = b, (b is an element of R(A(D))) 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.