The span of singular tuples of a tensor beyond the boundary format
Permanent link
https://hdl.handle.net/10037/34918Date
2023-05-10Type
Journal articleTidsskriftartikkel
Peer reviewed
Abstract
In this paper, we study the linear span of singular k-tuples of a generic tensor. Its dimension also depends only on the tensor format. In particular, we concentrate on special order three tensors and order-k tensors of format (2, ..., 2, n). . As a consequence, if again we fix the first k - 1 dimensions n > 3 and let nk increase, we show that in these special formats, the dimension of the linear span stabilizes as well, but at some concise non-sub-boundary format. We conjecture that this phenomenon holds for an arbitrary format with k>3. . Finally, we provide equations for the linear span of singular triples of a generic order three tensor T of some special non-sub-boundary format. From these equations, we conclude that T belongs to the linear span of its singular triples, and we conjecture that this is the case for every tensor format.