On some tensor inequalities based on the t-product

被引：3

作者：

Cao, Zhengbang ^{[1
]}

Xie, Pengpeng ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2023年 / 71卷 / 03期

基金：

中国国家自然科学基金;

关键词：

t-positive semidefiniteness; tensor power; tensor norm inequality; t-eigenvalue; FACTORIZATION;

D O I：

10.1080/03081087.2022.2032567

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known arithmetic-geometric mean inequality, Holder inequality, and Minkowski inequality are generalized to tensors. Furthermore, we obtain some t-eigenvalue inequalities.

引用

页码：377 / 390

页数：14

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