The Perurbation Of The Drazin Inverse Of Tensors Of Tensors Based On The T-product And Its Application

In this paper,we mainly study the perturbation theory of T-Drazin inverse and its application in T-linear system,with the definitions and decomposition of the tensor for T-product,such as T-Drazin inverse,T-Jordan Decomposition,and so on.Finally,we discuss acute perturbation of T-Drazin inverse.Firstly,we give the perturbation analysis of T-Drazin inverse by T-Jordan De-composition and two-sided condition,then the examples are given.After that,the perturbation theory of T-Drazin inverse is discussed by T-block decomposition and one-sided condition.And the examples are given.Secondly,we discuss one applica-tion in T-linear system for perturbed A and b of A*x=b based on the T-product.Then the perturbations of solutions of the T-linear system are discussed.Finally,the definition of the acute perturbation is given by using the spectral radius of the difference between the projection of the tensor and the projection of the perturded tensor based on the T-product.According to the T-core nilpotent decomposition and the definition of spectral of the tensor,equivalent conditions of stable pertur-bation of T-Drazin inverse are obtained,and equivalent conditions between acute perturbation and stable perturbation of T-Drazin inverse are given.