An S-type eigenvalue localization set for tensors

An S-type eigenvalue localization set for a tensor is given by breaking N={1,2,⋯,n} into disjoint subsets S and its complement. It is shown that the new set is tighter than those provided by Qi (2005) [21] and Li et al. (2014) [13]. As applications of the results, a checkable sufficient condition for the positive definiteness of tensors and a checkable sufficient condition of the positive semi-definiteness of tensors are given.