  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 L. Qi (Journal of Symbolic
Computation 40 (2005) 1302-1324) and Li et al. (Numer. Linear Algebra Appl. 21
(2014) 39-50). 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.
