Sets computing the symmetric tensor rank

2012/02/14 by Edoardo Ballico, Ballico, Edoardo, Luca Chiantini +1
Engineering · Mathematics · Medicine · #14N05 #15A69 #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry (math.AG) #FOS: Mathematics #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1202.3066

openalex publication_date 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let n_d denote the degree d Veronese embedding of a projective space P^r. For any symmetric tensor P, the 'symmetric tensor rank' sr(P) is the minimal cardinality of a subset A of P^r, such that n_d(A) spans P. Let S(P) be the space of all subsets A of P^r, such that n_d(A) computes sr(P). Here we classify all P in Pⁿ such that sr(P) < 3d/2 and sr(P) is computed by at least two subsets. For such tensors P, we prove that S(P) has no isolated points.

Citations

• Tensor Decompositions and Applications

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