An eigenvalue localization set for tensors and its applications

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 [Formula: see text]-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 [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.