In this paper, it is proved that (strict) copositivity of a symmetric tensor
A is equivalent to the fact that every principal sub-tensor of
A has no a (non-positive) negative H++-eigenvalue. The
necessary and sufficient conditions are also given in terms of the
Z++-eigenvalue of the principal sub-tensor of the given tensor. This
presents a method of testing (strict) copositivity of a symmetric tensor by
means of the lower dimensional tensors. Also the equivalent definition of
strictly copositive tensors is given on entire space Rn.Comment: 13 pages. arXiv admin note: text overlap with arXiv:1302.608