C-乘积下的张量广义逆  

The Generalized Inverses of Tensors via the C-product

作　　者：靳宏伟[1,2] 徐淑敏 江鸿杰 刘晓冀 JIN Hongwei;XU Shumin;JIANG Hongjie;LIU Xiaoji(School of Mathematical Sciences;Center for Applied Mathematics of Guangxi,Guangxi Minzu University,Nanning 530006,China;School of Computer Engineering,Shangqiu University,Shangqiu 476000,Henan,China;School of Education,Guangxi Vocational Normal University,Nanning 530007,China)

机构地区：[1]广西民族大学数学科学学院 [2]广西民族大学应用数学中心,南宁530006 [3]商丘学院计算机工程学院,河南商丘476000 [4]广西职业师范学院教育学院,南宁530007

出　　处：《数学年刊(A辑)》2024年第4期437-468,共32页Chinese Annals of Mathematics

基　　金：广西自然科学基金(No.2024GXNSFAA010503);广西科技基地与人才专项(No桂科AA24010005);国家自然科学基金(No.12261027)的资助。

摘　　要：作者主要研究了C-乘积下的张量广义逆.首先,给出了C-乘积下张量的Moore-Penrose逆,Drazin逆和沿张量逆的定义,并通过使用张量的几种分解形式给出了张量广义逆的其它表达式.此外,建立了张量的Moore-Penrose逆,Drazin逆和沿张量逆的算法.最后,给出了张量的群逆在马尔可夫链上的应用.This paper studies the issues about the generalized inverses of tensors under the C-product.The aim of this paper is fourfold.Firstly,this paper presents the definition of the Moore-Penrose inverse,Drazin inverse of tensors under the C-product.Moreover,the inverse along a tensor is also introduced.Secondly,this paper gives some other expressions of the generalized inverses of tensors by using several decomposition forms of tensors.In addition,the algorithms for computing the Moore-Penrose inverse,Drazin inverse of tensors and the inverse along a tensor are established.Finally,the application of group inverse of tensor to Markov chains is given.

关 键 词：C-乘积 张量 MOORE-PENROSE逆 DRAZIN逆 沿张量逆 

分 类 号：O151[理学—数学]