A NEW CLASS OF POSITIVE SEMI-DEFINITE TENSORS

被引：1

作者：

Xu, Yi ^{[1
]}

Liu, Jinjie ^{[2
]}

Qi, Liqun ^{[2
]}

机构：

[1] Southeast Univ, Math Dept, 2 Sipailou, Nanjing 210096, Jiangsu, Peoples R China

[2] Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China

来源：

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION | 2020年 / 16卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Positive (semi-)definite tensor; completely positive tensor; H-eigenvalue; MO-tensor; MO-like tensor; Sup-MO value; EIGENVALUES;

D O I：

10.3934/jimo.2018186

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and essential MO tensor. They are proved to be positive definite tensors. Especially, the smallest H-eigenvalue of a Sup-MO tensor is positive and tends to zero as the dimension tends to infinity, and an essential MO tensor is also a completely positive tensor.

引用

页码：933 / 943

页数：11

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