Brualdi-type inequalities on the minimum eigenvalue for the Fan product of M-tensors

Gang Wang; Yiju Wang; Yuan Zhang

doi:10.3934/jimo.2019069

Article Contents

2020, Volume 16, Issue 5: 2551-2562. Doi: 10.3934/jimo.2019069

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Brualdi-type inequalities on the minimum eigenvalue for the Fan product of M-tensors

School of Management Science, Qufu Normal University, Rizhao, Shandong 276826, China

^* Corresponding author: Gang Wang
^* Corresponding author: Gang Wang

Received: August 31, 2018

Revised: February 28, 2019

Early access: July 2019

Published: August 2020

This work was supported by the Natural Science Foundation of China (11671228) and the Natural Science Foundation of Shandong Province (ZR2016AM10)

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Abstract

In this paper, we focus on some inequalities for the Fan product of $ M $-tensors. Based on Brualdi-type eigenvalue inclusion sets of $ M $-tensors and similarity transformation methods, we establish Brualdi-type inequalities on the minimum eigenvalue for the Fan product of two $ M $-tensors. Furthermore, we discuss the advantages of different Brualdi-type inequalities. Numerical examples verify the validity of the conclusions.

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Mathematics Subject Classification: Primary: 15A18, 15A42.

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