On the tensor rank of $3\times 3$ permanent and determinant

zbMath1470.15018arXiv1801.00496MaRDI QIDQ5003343

Siddharth Krishna, Visu Makam

Publication date: 21 July 2021

Full work available at URL: https://arxiv.org/abs/1801.00496

zbMATH Keywords

determinantpermanenttensor rankborder rank

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Multilinear algebra, tensor calculus (15A69)

Related Items (2)

Tensors in computations ⋮ An improved upper bound for the Waring rank of the determinant

Uses Software

• GitHub

Cites Work

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• Nontriviality of equations and explicit tensors in \(\mathbb{C}^m \otimes \mathbb{C}^m \otimes \mathbb{C}^m\) of border rank at least \(2m - 2\)
• Gaussian elimination is not optimal
• Product Ranks of the 3 × 3 Determinant and Permanent
• On non-commutative rank and tensor rank
• Barriers for Rank Methods in Arithmetic Complexity
• Explicit tensors of border rank at least 2d−2 in K^d ⊗ K^d ⊗ K^d in arbitrary characteristic
• Multiplying matrices faster than coppersmith-winograd

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