# American Institute of Mathematical Sciences

September  2020, 16(5): 2551-2562. doi: 10.3934/jimo.2019069

## 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

Received  September 2018 Revised  March 2019 Published  July 2019

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

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.

Citation: Gang Wang, Yiju Wang, Yuan Zhang. Brualdi-type inequalities on the minimum eigenvalue for the Fan product of M-tensors. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2551-2562. doi: 10.3934/jimo.2019069
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