The Perturbation For Two Kinds Of Generalized Inverses Of Tensors Based On The T-product

In this paper,the perturbation for core-EP inverse and Moore-Penrose inverse of tensors are discussed and analyzed by using the related concepts and lemmas of T-product of tensors.Firstly,we introduce the concept of core-EP inverse of tensor based on the T-product and discuss its existence and uniqueness.The core-EP decomposition of tensors is given by the Schur decomposition of tensors based on the T-product,and then we get the expression of core-EP inverse of tensors and study properties and characteristics of core-EP inverse of tensors.The equivalent conditions for stable perturbation and acute perturbation of core-EP inverse of tensors are given.Next,we give the definitions of acute perturbation and stable perturbation for Moore-Penrose inverse of tensors based on the T-product,and the equivalent conditions of stable perturbation and acute perturbation are given.At last,we give the example to demonstrate the result.