Explicit tensors of border rank at least 2d-2 in K^d \⊗ K^d\n \⊗ K^d in arbitrary characteristic

2017/09/18 by Harm Derksen, Derksen, Harm, Visu Makam +1
Engineering · Mathematics · Physics and Astronomy · #15A69 #Advanced Numerical Methods in Computational Mathematics #Black Holes and Theoretical Physics #FOS: Mathematics #Rings and Algebras (math.RA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1709.06131

openalex publication_date 2017/09/18 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

For tensors in \ℂ^d \⊗ \ℂ^d \⊗ \ℂ^d,\nLandsberg provides non-trivial equations for tensors of border rank 2d-3 for\nd even and 2d-5 for d odd were found by Landsberg. In previous work, we\nobserve that Landsberg's method can be interpreted in the language of tensor\nblow-ups of matrix spaces, and using concavity of blow-ups we improve the case\nfor odd d from 2d-5 to 2d-4. The purpose of this paper is to show that\nthe aforementioned results extend to tensors in K^d \⊗ K^d \⊗ K^d\nfor any field K.\n

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