| 靳宏伟,徐淑敏,江鸿杰,刘晓冀.C-乘积下的张量广义逆[J].数学年刊A辑,2024,45(4):437~468 |
| C-乘积下的张量广义逆 |
| The Generalized Inverses of Tensors via the C-product |
| Received:November 04, 2022 Revised:November 28, 2024 |
| DOI：10.16205/j.cnki.cama.2024.0030 |
| 中文关键词: C-乘积 张量 Moore-Penrose逆 Drazin逆 沿张量逆 |
| 英文关键词:C-product, Tensors, Moore-Penrose inverse, Drazin inverse,
Inverse along a tensor |
| 基金项目: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) |
| Author Name | Affiliation | | JIN Hongwei | School of Mathematical Sciences
Center for Applied Mathematics of Guangxi,
Guangxi Minzu University, Nanning 530006, China. | | XU Shumin | School of Computer Engineering, Shangqiu University, Shangqiu 476000,
Henan, China. | | JIANG Hongjie | School of Mathematical Sciences
Center for Applied
Mathematics of Guangxi, Guangxi Minzu University, Nanning 530006, China. | | LIU Xiaoji | School of Education, Guangxi Vocational Normal University, Nanning 530007,
China. |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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