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

作　　者：王宏兴[1] 刘洁[1] Hong Xing WANG;Jie LIU(School of Mathematics and Physics,Guangri University for Nationalities,Nanning 530006,P.R.China)

机构地区：[1]广西民族大学数学与物理学院,南宁530006

出　　处：《数学学报（中文版）》2022年第5期827-840,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(12061015);广西科技基地和人才专项基金(桂科AD19245148);广西硕士研究生创新项目(YCSW2021146);广西民族大学相思湖青年学者创新团队(2019RSCXSHQN03)。

摘　　要：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.

关 键 词：T-乘积 T-DMP逆 T-CMP逆 CAYLEY-HAMILTON定理 T-Drazin逆 

分 类 号：O151[理学—数学]