Practical Criteria for <inline-formula><math display="inline"><semantics><mi mathvariant="script">H</mi></semantics></math></inline-formula>-Tensors and Their Application

Abstract

Identifying the positive definiteness of even-order real symmetric tensors is an important component in tensor analysis. H-tensors have been utilized in identifying the positive definiteness of this kind of tensor. Some new practical criteria for identifying H-tensors are given in the literature. As an application, several sufficient conditions of the positive definiteness for an even-order real symmetric tensor were obtained. Numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords

• ℋ-tensors
• real symmetric tensors
• positive definiteness
• irreducible