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arXiv · 1811.01865

Identifiability for a class of symmetric tensors

Elena Angelini·Luca Chiantini·Andrea Mazzon
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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.

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Elena Angelini, Luca Chiantini, Andrea Mazzon. 2019-07-22. Identifiability for a class of symmetric tensors. https://doi.org/10.1007/s00009-019-1363-5

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