On tensors of border rank l in \C^{m× n× l}

2010/03/09 by Shmuel Friedland, Friedland, Shmuel
Engineering · Mathematics · Medicine · #14A25 #14P10 #15A69 #Advanced Neuroimaging Techniques and Applications #Algebraic Geometry (math.AG) #Elasticity and Material Modeling #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1003.1968

openalex publication_date 2010/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study tensors in \C^{m× n× l} whose border rank is l. We characterize the tensors in \C^{3× 3× 4} and in \C^{4× 4× 4} of border rank 4 at most.

Related

• Explicit tensors of border rank at least 2n-1
• The border rank of the 4 × 4 determinant tensor is twelve
• Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in C^m⊗ C^m⊗ C^m
• Explicit tensors of border rank at least 2d-2 in K^d \⊗ K^d\n \⊗ K^d in arbitrary characteristic
• Border rank bounds for GL(V)-invariant tensors arising from matrices of constant rank