T-乘积下张量广义逆及其广义Cayley-Hamilton定理

The Generalized Inverses of Tensors and Generalized Cayley-Hamilton Theorem Based on the T-Product

本文通过张量在T-乘积下的T-Moore-Penrose逆、T-Drazin逆以及T-corenilpotent分解定理,引入三阶F-square(正面方的)张量在T-乘积下的T-DMP逆与TCMP逆的定义,同时给出它们的若干刻画和性质.最后将三阶张量的Cayley-Hamilton定理推广到张量的T-Drazin逆与T-DMP逆上,并给出例子进行验证.

We define the T-DMP inverse and T-CMP inverse of third-order F-square tensors by using the T-Moore-Penrose inverse,T-Drazin inverse and T-core-nilpotent decomposition theorem of tensors via the T-product.Then,we present some characterizations and properties.Finally,the Cayley-Hamilton theorem of third-order tensors is extended to T-Drazin inverses and T-DMP inverses.Examples are also given to illustrate these theorems.