On the hyperdeterminant for 2×2×3 arrays

DOI10.1080/03081087.2011.634412zbMath1254.15009OpenAlexW1975753518MaRDI QIDQ5200328

Murray R. Bremner

Publication date: 5 November 2012

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

Full work available at URL: https://doi.org/10.1080/03081087.2011.634412

zbMATH Keywords

Lie algebrasrepresentation theoryinvariant theorymultilinear algebrahyperdeterminantmultidimensional arrays

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Multilinear algebra, tensor calculus (15A69)

Related Items (4)

Fundamental invariants for the action of $SL_3(\mathbb {C}) \times SL_3(\mathbb {C}) \times SL_3(\mathbb {C})$ on $3 \times 3 \times 3$ arrays ⋮ Rank classification of tensors over ⋮ Unnamed Item ⋮ Canonical forms of 2 × 2 × 2 and 2 × 2 × 2 × 2 arrays over 𝔽₂and 𝔽₃

Cites Work

• Tensor Decompositions and Applications
• Kruskal's polynomial for \(2 \times{}2 \times{}2\) arrays and a generalization to \(2 \times{}n \times{}n\) arrays
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• Hyperdeterminants
• The rank of a 2 × 2 × 2 tensor
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Naive Lie Theory
• Subtracting a best rank-1 approximation may increase tensor rank

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