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Article Dans Une Revue Journal of Symbolic Computation Année : 2022

The span of singular tuples of a tensor beyond the boundary format

Résumé

We study the dimension of the span of singular tuples of a tensor $T$ without assuming that the ambient tensor space is of sub-boundary format. In particular, we concentrate on special order three tensors as well as order-$k$ tensors of format $(2,\ldots,2,n)$. In some of the mentioned formats, we show that the tensor $T$ belongs to the span of its singular $k$-tuples. Furthermore, we conjecture that the dimension of the span of singular $k$-tuples stabilizes beyond the boundary format when $k>3$.

Dates et versions

hal-04072789 , version 1 (18-04-2023)

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Luca Sodomaco, Ettore Teixeira Turatti. The span of singular tuples of a tensor beyond the boundary format. Journal of Symbolic Computation, 2022, 120, pp.102230. ⟨10.1016/j.jsc.2023.102230⟩. ⟨hal-04072789⟩
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