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. (c) 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc-nd/4.0/).
Decomposition loci of tensors / Bernardi, A; Oneto, A; Santarsiero, P. - In: JOURNAL OF SYMBOLIC COMPUTATION. - ISSN 0747-7171. - 131:(2025), pp. 102451-102451. [10.1016/j.jsc.2025.102451]
Decomposition loci of tensors
Oneto, A;Santarsiero, P
2025-01-01
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. (c) 2025 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc-nd/4.0/).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
