New criteria for H $\mathcal{H}$ -tensors and an application

Abstract

Abstract Some new criteria for H $\mathcal{H}$ -tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. The advantages of the results obtained are illustrated by numerical examples.

Keywords

• H $\mathcal{H}$ -tensor
• symmetric tensor
• positive definiteness
• irreducible
• nonzero elements chain