The Criteria for Nonsingular H-tensors and its Applications

Tensors are the high order promotion of matrices, and have been widely used in engineering and scientific research. H-tensor is an important tensor, but it is not easy to determine whether a tensor is a nonsingular H-tensor. In this paper, using to the relations of diagonally dominant tensors and H-tensors, some criteria for identifying H-tensors are given by the skills of magnifying and shrinking of inequalities. Finally, the validity of our results is illustrated by some numerical examples, furthermore, we consider the positive definiteness for an even-order real symmetric tensor using nonsingular H-tensors.