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
收藏
页码：933 / 943
页数：11
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