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

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.