On the generic and typical ranks of 3-tensors
Algebraic Geometry
2011-01-25 v5 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.0805.3777,
title = {On the generic and typical ranks of 3-tensors},
author = {Shmuel Friedland},
journal= {arXiv preprint arXiv:0805.3777},
year = {2011}
}
Comments
24 pages