张量Lowner偏序与其Moore-Penrose逆的关系  

Relationships between Lowner Partial Orders of Tensors and Their Moore-Penrose Inverses

作　　者：刘喜富 罗宇 LIU Xifu;LUO Yu(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2023年第2期84-88,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金项目(No.cstc2021jcyj-msxmX0195);重庆市教育委员会科学技术研究计划项目(No.KJQN202100505)。

摘　　要：[目的]研究爱因斯坦积下L?wner偏序A≥B和A>B与它们的Moore-Penrose逆的关系。[方法]通过张量特征值、值域及Moore-Penrose逆来研究张量Lowner偏序A≥B和A>B。[结果]得到了一些关于偏序A≥B和A>B的基本性质和充要条件。[结论]Lowner偏序A≥B和A>B成立的充要条件表明,矩阵L?wner偏序的性质能够推广到张量上。[Purposes]The goal is to study the relationships between Lowner partial orders A≥B and A>B and their Moore Penrose inverses.[Methods]By using the eigenvalues,range,Moore-Penrose inverse of tensor,the Lowner partial orders A≥B and A>B are studied.[Findings]Some basic properties and equivalent conditions of partial orders A≥B and A>B are obtained.[Conclusions]The sufficient and necessary conditions of Lowner partial order A≥B and A>B show that the properties of matrix Lownerpartialordering can begeneralized totensors.

关 键 词：爱因斯坦积 张量 Lowner偏序 MOORE-PENROSE逆 

分 类 号：O151[理学—数学]