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.

arXiv comment25 pages, 3 figures

References in corpus (11)

• Quantum Entanglement in Fermionic Lattices
• The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement
• Computing symmetric rank for symmetric tensors
• Eigenvectors of tensors and algorithms for Waring decomposition
• Bipartite entanglement in fermion systems
• Ideals of varieties parameterized by certain symmetric tensors
• Tensor ranks on tangent developable of Segre varieties
• Algebraic Geometry tools for the study of entanglement: an application to spin squeezed states
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
• Waring-like decompositions of polynomials - 1
• A note on the cactus rank for Segre-Veronese varieties

Cited by in corpus (4)

• The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
• Identifiability and singular locus of secant varieties to Grassmannians
• Identifiability and singular locus of secant varieties to spinor varieties
• Restricted Secant Varieties of Grassmannians