Skew-Symmetric Tensor Decomposition

Abstract

We introduce the ``skew apolarity lemma'' and we use it to give algorithms for the skew-symmetric rank and the decompositions of tensors in {${\bigwedge }^d{V}_{\mathbb{C}}$ with $d\le 3$ and $\dim V_{\mathbb{C}}\le 8$}. New algorithms to compute the rank and a minimal decomposition of a tritensor are also presented.

25 pages, 3 figures