Skew-Symmetric Tensor Decomposition

Enrique Arrondo (1) , Alessandra Bernardi (2) , Pedro Macias Marques (3) , Bernard Mourrain (4)

1 UCM - Universidad Complutense de Madrid = Complutense University of Madrid [Madrid]
2 Department of mathematics/Dipartimento di Matematica [Univ. Trento]
3 Departamento de Matemática da Universidade de Évora
4 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

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

Domaines: Géométrie algébrique [math.AG]

Enrique Arrondo, Alessandra Bernardi, Pedro Macias Marques, Bernard Mourrain. Skew-Symmetric Tensor Decomposition. Communications in Contemporary Mathematics, 2019, 23 (02), pp.1950061. ⟨10.1142/S0219199719500615⟩. ⟨hal-01940005⟩