An eigenvalue localization set for tensors and its applications

Abstract

Abstract A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Li et al. (Linear Algebra Appl. 481:36-53, 2015) and Huang et al. (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of M $\mathcal{M}$ -tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huang et al., the advantage of our results is that, without considering the selection of nonempty proper subsets S of N = { 1 , 2 , … , n } $N=\{1,2,\ldots,n\}$ , we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of M $\mathcal{M}$ -tensors. Finally, numerical examples are given to verify the theoretical results.

Keywords

• M $\mathcal{M}$ -tensors
• nonnegative tensors
• minimum eigenvalue
• localization set