Research On The CMP Inverse Of Tensors Via The T-product

In this paper,by using the Discrete Fourier Transform and the T-Schur decomposition of tensors,we study characteristics,algorithms and perturbation of the CMP inverse of tensors via the T-product(T-CMP inverse).Firstly,we study characteristics of the T-CMP inverse based on the concepts and lemmas related to tensors via the T-product.Equivalent descriptions,range space and null space of the T-CMP inverse are given.In addition,an expression for the T-CMP inverse under the T-Schur decomposition is given.Then we use this expression to study the relationship between the T-CMP inverse and other generalized inverses of tensors,as well as equivalent conditions for a tensor to be a core-EP tensor.Secondly,we propose the successive tensor squaring algorithm and Fourier-Gauss-Jordan method for computing the T-CMP inverse of tensors,then some examples of using these algorithms to compute the T-CMP inverse are given.Finally,after adding a perturbation tensor which satisfies two-sided condition to a tensor,the perturbation bound of the T-CMP inverse is analyzed.The results of the two-sided perturbation of the T-CMP inverse are illustrated by examples.