p-Norm SDD tensors and eigenvalue localization

Abstract

Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors), which is a subclass of strong H $\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016) in some case. Based on this set, we give a checkable sufficient condition for the positive (semi)definiteness of an even-order symmetric tensor.

Keywords

• p-norm SDD tensor
• strong H $\mathcal{H}$ -tensor
• positive (semi)definiteness
• eigenvalue localization