T- 乘积下张量的T-CS 逆及其偏序

文薇, 王宏兴^*, 刘娜, 靳宏伟

出版日期:2023-06-28 发布日期:2023-06-27
通讯作者: 王宏兴; E-mail: winghongxing0902@163.com E-mail:winghongxing0902@163.com
基金资助:
国家自然科学基金项目(No. 12061015), 广西自然科学基金项目(No. 2018GXNSFDA281023)和

广西民族大学相思湖青年学者创新团队项目(No. 2019RSCXSHQN03)资助.

Wen Wei, Wang Hongxing^*,Liu Na, Jin Hongwei

Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning 530006, China

摘要：

张量广义逆与张量偏序是张量理论的重要组成部分.

在 T-乘积下, 本文引入三阶张量 T-CS 逆, 给出该逆的若干刻画和性质,

并应用该逆引入新的二元关系: ${\small\textcircled{S}}$ 序.

在 i-EP 张量集合中, 该 ${\small\textcircled{S}}$ 序与 T-星序等价.

进一步, 本文应用 ${\small\textcircled{S}}$ 序引入 T-CS 偏序并给出其刻画.

关键词: T-乘积, T-CS 逆, T-CS 偏序

Abstract:

The generalized inverse and partial order of tensor are important components of tensor theory.

In this paper, we introduce the T-CS inverse of third-order tensor,

obtain some characterizations and properties of it under the T-product,

and apply it to

introduce a new binary relation:

the ${\textcircled{S}}$ order, which is equivalent to the T-star order under the set of i-EP tensors.

Based on the ${\textcircled{S}}$ order, we further introduce the T-CS partial order and give some characterizations of it.

Key words: T-product, T-CS inverse, T-CS partial order

文薇, 王宏兴, 刘娜, 靳宏伟. T- 乘积下张量的T-CS 逆及其偏序[J]. 数学理论与应用, 2023, 43(2): 48-67.

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