Abstract
In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal sub-tensors has no (non-positive) negative (Formula presented.) -eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of (Formula presented.) -eigenvalues of the principal sub-tensors of that tensor. This presents a method for testing (strict) copositivity of a symmetric tensor by means of lower dimensional tensors. Also, an equivalent definition of strictly copositive tensors is given on the entire space (Formula presented.).
| Original language | English |
|---|---|
| Pages (from-to) | 120-131 |
| Number of pages | 12 |
| Journal | Linear and Multilinear Algebra |
| Volume | 63 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2015 |
Keywords
- copositive tensors
- H -eigenvalue ++
- principal sub-tensor
- Z -eigenvalue ++
ASJC Scopus subject areas
- Algebra and Number Theory