We study the generic and typical ranks of 3-tensors of dimension l, m, 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 veried numerically for l; m; ≤ n 14. We also discuss the typical ranks over the real numbers, and give an example of an innite family of 3-tensors of the form l = m; n = (m-1)2 + 1;m = 3; 4,..., which have at least two typical ranks.
NOTICE: this is the author’s version of a work that was accepted for publication in Linear Algebra and Its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and Its Applications, 436(3)DOI: 10.1016/j.laa.2011.05.008 Published: FEB 1 2012