Kruskal’s theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called Kruskal-ranks of the product tensors are large. In this work, we prove a result in which the Kruskal-rank condition of Kruskal’s theorem is weakened to the standard notion of rank, and the conclusion is relaxed to a statement on the linear dependence of the product tensors. Our result implies a generalization of Kruskal’s theorem. Several adaptations and generalizations of Kruskal’s theorem have already been obtained, but most of these results still cannot certify uniqueness when the Kruskal-ranks are below a certain threshold. Our generalization contains several of these results, and can certify uniqueness below this threshold. This talk is based on joint work with Fedor Petrov [https://arxiv.org/pdf/2103.15633.pdf].
Copyright. All Rights Reserved.