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 $k>3$.