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Article Dans Une Revue Linear Algebra and its Applications Année : 2020

On minimal decompositions of low rank symmetric tensors

Résumé

We use an algebraic approach to construct minimal decompositions of symmetric tensors with low rank. This is done by using Apolarity Theory and by studying minimal sets of reduced points apolar to a given symmetric tensor, namely, whose ideal is contained in the apolar ideal associated to the tensor. In particular, we focus on the structure of the Hilbert function of these ideals of points. We give a procedure which produces a minimal set of points apolar to any symmetric tensor of rank at most 5. This procedure is also implemented in the algebra software Macaulay2.
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Dates et versions

hal-01803571 , version 1 (30-05-2018)

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Bernard Mourrain, Alessandro Oneto. On minimal decompositions of low rank symmetric tensors. Linear Algebra and its Applications, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩. ⟨hal-01803571⟩
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