Sharp Brauer-Type Eigenvalue Inclusion Theorems for Tensors

Abstract

In this paper, some new Brauer-type eigenvalue inclusion theroems are established for general tenors. We show that new eigenvalue inclusion sets are sharper than classical results. As applications obtain bounds for the largest eigenvalue of a nonnegative tensor, which achieve tighter bounds than existing bounds. Furthermore, based on these eigenvalue inclusion theorems, we present several sufficient conditions to test positive definiteness and positive semi-definiteness of tensors.