Characteristics Of T-core Inverse And Its Perturbation Analysis Based On The T-product

In this paper,we mainly study the Tensor-core(T-core)inverse based on the T-product.First,the H-S decomposition of the tensor under the T-product is given,then,the H-S decomposition form of T-Moore-Penrose inverse and T-group inverse are given.Further,we introduce the definition of the T-core inverse.By H-S decomposition,the existence and uniqueness and other properties of T-core inverse are proved.Next,several representations of T-core inverse are given.In addition,we present perturbation analysis with one-sided and two-sided conditions for the T-core inverse,and two examples are given to illustrate the perturbation results,respectively.Next,the condition(C1,*)of tensors under the T-product is defined,and the characteristics and the representation of T-core inverse under the condition(C1,*)are introduced.Finally,the perturbation analysis of T-core inverse under the condition(C1,*)is studied and two examples are given to illustrate the perturbation results.