A hyperdeterminant for 2 x 2 x 3 arrays

2011/06/15 by Murray R. Bremner, Bremner, Murray R.
Computer Science · Mathematics · Physics and Astronomy · #15A72 #Digital Filter Design and Implementation #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Tensor decomposition and applications #hep-th #math-ph #math.MP #math.RA #math.RT #msc:15A72

paper · pdf · doi:10.48550/arxiv.1106.2988

11 pages

arxiv created 2011/06/15 · openalex publication_date 2011/06/15 · arxiv updated 2011/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the representation theory of Lie algebras and computational linear algebra to determine the simplest nonconstant invariant polynomial in the entries of a general 2 x 2 x 3 array. This polynomial is homogeneous of degree 6 and has 66 terms with coefficients 1, -1, 2, -2 in the 12 indeterminates x_ijk where i,j = 1,2 and k = 1,2,3. This invariant can be regarded as a natural generalization of Cayley's hyperdeterminant for 2 x 2 x 2 arrays.

Citations

• Tensor Decompositions and Applications

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