On generic identifiability of symmetric tensors of subgeneric rank

By Luca Chiantini, Giorgio Ottaviani, Nick Vannieuwenhoven. 2015

97 citations recorded by the source corpus.

We prove that the general symmetric tensor in $S^d {\mathbb C}^{n+1}$ of rank r is identifiable, provided that r is smaller than the generic rank. That is, its Waring decomposition as a sum of r powers of linear forms is unique. Only three exceptional cases arise, all of which were known in the literature. Our original contribution regards the case of cubics ($d=3$), while for $d\ge 4$ we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/27f5c709448bd931b0829f49071b566e02d277fe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Alessandra Bernardi
2. A. Oneto
3. Alessandro Gimigliano
4. Enrico Carlini
5. M. Catalisano

In Computational Mechanics

1. Alessandra Bernardi

In Computational Theory and Mathematics

1. Alessandra Bernardi
2. M. Catalisano
3. A. Oneto
4. Alessandro Gimigliano
5. Enrico Carlini

Citations in the corpus

• The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “Generic identifiability is quite rare as a phenomenon, and it has been largely investigated; in particular, we refer to [200, 198, 199, 197, 201, 202, 189, 12].”