Nonsingular H-tensor and its criteria

Abstract

H-tensor is a new developed concept in tensor analysis and it is an extension of H-matrix and M-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of nonsingular H-tensors are established in the literature. However, these conditions can not be used as a criteria to identify nonsingular H-tensors as they are hard to verify. In this paper, based on the diagonal product dominance and S diagonal product dominance of a tensor, we establish some new implementable criteria in identifying nonsingular H-tensors. The positive definiteness of nonsingular H-tensors with positive diagonal entries is also discussed in this paper. The obtained results extend the corresponding conclusions for nonsingular H-matrices and improve the existing results for nonsingular H-tensors.