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arXiv · 1106.2988

A hyperdeterminant for 2 x 2 x 3 arrays

Murray R. Bremner
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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.

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Murray R. Bremner. 2011-06-15. A hyperdeterminant for 2 x 2 x 3 arrays. https://arxiv.org/abs/1106.2988

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