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}
}