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arXiv · 2407.18138

Decomposition loci of tensors

Alessandra Bernardi·Alessandro Oneto·Pierpaola Santarsiero
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Abstract

The decomposition locus of a tensor is the set of rank-one tensors appearing in a minimal tensor-rank decomposition of the tensor. For tensors lying on the tangential variety of any Segre variety, but not on the variety itself, we show that the decomposition locus consists of all rank-one tensors except the tangency point only. We also explicitly compute decomposition loci of all tensors belonging to tensor spaces with finitely many orbits with respect to the action of product of general linear groups.

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Alessandra Bernardi, Alessandro Oneto, Pierpaola Santarsiero. 2024-07-25. Decomposition loci of tensors. https://arxiv.org/abs/2407.18138

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