Some new inequalities for the minimum H-eigenvalue of nonsingular M-tensors

This paper is devoted to deriving some new upper and lower bounds for the minimum H-eigenvalue of irreducible nonsingular M-tensors. We demonstrate that the proposed bounds improve some existing ones and numerical examples are given to illustrate this fact. Additionally, we extend these bounds to general nonsingular M-tensors. The other main results in this paper is to provide sharper Ky Fan theorem and comparison theorem for nonsingular M-tensors which are better than the corresponding ones obtained by He and Huang (2014) [12].