English

Identifiability for a class of symmetric tensors

Algebraic Geometry 2019-07-23 v2

Abstract

We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree 7, we use the analysis of the Hilbert function of a finite projective set, and the Cayley-Bacharach property, to prove that, when the Kruskal's rank of a decomposition of T are maximal (a condition which holds outside a Zariski closed set of measure 0), then the tensor T is identifiable, i.e. the decomposition is unique, even if the rank lies beyond the range of application of both the Kruskal's and the reshaped Kruskal's criteria.

Keywords

Cite

@article{arxiv.1811.01865,
  title  = {Identifiability for a class of symmetric tensors},
  author = {Elena Angelini and Luca Chiantini and Andrea Mazzon},
  journal= {arXiv preprint arXiv:1811.01865},
  year   = {2019}
}