偶数阶张量core逆的性质和应用

数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 1-14.

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偶数阶张量core逆的性质和应用

王宏兴^1,*(),张晓燕^1,²()

¹ 广西民族大学数学与物理学院南宁 530006
² 湖南城市学院教师教育学院湖南益阳 413000

收稿日期:2020-02-01 出版日期:2021-02-26 发布日期:2021-01-29
通讯作者: 王宏兴,张晓燕 E-mail:winghongxing0902@163.com;1310362243@qq.com
作者简介:张晓燕, E-mail: 1310362243@qq.com
基金资助:
国家自然科学基金(61772006);广西自然科学基金(2018GXNSFAA138181);广西科技基地和人才专项基金(桂科AD19245148)

Properties and Applications of the Core Inverse of an Even-Order Tensor

Hongxing Wang^1,*(),Xiaoyan Zhang^1,²()

¹ School of Mathematics and Physics, Guangxi University for Nationalities, Nanning 530006
² School of Teacher Education, Hunan City University, Hunan Yiyang 413000

Received:2020-02-01 Online:2021-02-26 Published:2021-01-29
Contact: Hongxing Wang,Xiaoyan Zhang E-mail:winghongxing0902@163.com;1310362243@qq.com

摘要/Abstract

摘要：

张量广义逆是张量理论研究的重要内容之一.在近年张量广义逆研究的基础上，该文给出在爱因斯坦积下张量core逆的性质、张量偏序和张量方程 ${{\cal A}}{*}{{\cal X}}={{\cal B}}在条件{{\cal X}}∈{\Bbb{\cal R}}({{\cal A}}) $下的最小二乘解等.

关键词: core逆, 爱因斯坦积, 偏序, 张量方程

Abstract:

Tensor generalized inverse is one of the important contents of tensor theory research. In this paper, based on the research of tensor generalized inverse in recent years, we obtain some properties of the core inverse of tensor with the Einstein product, a tensor partial ordering based on the core inverse and the least-squares solution of $ {{\cal A}} {*}{{\cal X}}={{\cal B}}$ under condition ${{\cal X}}\in{\Bbb {\cal R}}({{\cal A}}) $.

Key words: Core inverse, Einstein product, Partial ordering, Tensor equation

中图分类号:

O151

王宏兴,张晓燕. 偶数阶张量core逆的性质和应用[J]. 数学物理学报, 2021, 41(1): 1-14.

Hongxing Wang,Xiaoyan Zhang. Properties and Applications of the Core Inverse of an Even-Order Tensor[J]. Acta mathematica scientia,Series A, 2021, 41(1): 1-14.

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偶数阶张量core逆的性质和应用

Properties and Applications of the Core Inverse of an Even-Order Tensor

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