T-乘积下张量的T-CS逆及其偏序  

CS Inverse and Partial Order of Tensors under T-Product

作　　者：文薇 王宏兴[1] 刘娜 靳宏伟[1] Wen Wei;Wang Hongxing;Liu Na;Jin Hongwei(Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Guangxi Minzu University,Nanning 530006,China)

机构地区：[1]广西民族大学数学与物理学院,广西混合计算与集成电路设计分析重点实验室,南宁530006

出　　处：《数学理论与应用》2023年第2期48-67,共20页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.12061015);广西自然科学基金项目(No.2018GXNSFDA281023);广西民族大学相思湖青年学者创新团队项目(No.2019RSCXSHQN03)资助。

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:S序.在i-EP张量集合中,该S序与T-星序等价.进一步,本文应用S序引入T-CS偏序并给出其刻画.The generalized inverse and partial order of tensor are important components of tensor theory.In this paper,we introduce the TCS inverse of thirdorder tensor,obtain some characterizations and properties of it under the Tproduct,and apply it to introduce a new binary relation:the Sorder,which is equivalent to the Tstar order under the set of iEP tensors.Based on the Sorder,we further introduce the TCS partial order and give some characterizations of it.

关 键 词：T-乘积 T-CS逆 T-CS偏序 

分 类 号：O183.2[理学—数学]