On the generic and typical ranks of 3-tensors

Details On the generic and typical ranks of 3-tensors On the generic and typical ranks of 3-tensors

2008-05-24

arxiv.org/abs/0805.3777v5

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We study the generic and typical ranks of 3-tensors of dimension l x m x n using results from matrices and algebraic geometry. We state a conjecture about the exact values of the generic rank of 3-tensors over the complex numbers, which is verified numerically for l,m,n not greater than 14. We also discuss the typical ranks over the real numbers, and give an example of an infinite family of 3-tensors of the form l=m, n=(m-1)^2+1, m=3,4,..., which have at least two typical ranks.

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