Explicit tensors of border rank at least 2d−2 in Kd ⊗ Kd ⊗ Kd in arbitrary characteristic

DOI10.1080/03081087.2018.1484419zbMath1425.15023arXiv1709.06131OpenAlexW2810245715WikidataQ114100608 ScholiaQ114100608MaRDI QIDQ5239278

Visu Makam, H. G. J. Derksen

Publication date: 22 October 2019

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.06131

zbMATH Keywords

lower boundsborder ranklinear subspaces of matricesKoszul flatteningstensor blow-up

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Matrix equations and identities (15A24) Multilinear algebra, tensor calculus (15A69)

Related Items (2)

On the tensor rank of $3\times 3$ permanent and determinant ⋮ Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)

Cites Work

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• On the nuclear norm and the singular value decomposition of tensors
• Polynomial degree bounds for matrix semi-invariants
• The permanent of a square matrix
• Nontriviality of equations and explicit tensors in \(\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m\) of border rank at least \(2m - 2\)
• Product Ranks of the 3 × 3 Determinant and Permanent
• New lower bounds for the border rank of matrix multiplication
• Relative invariants of 3 × 3 matrix triples^∗
• On non-commutative rank and tensor rank

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