Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773422 | Linear Algebra and its Applications | 2017 | 12 Pages |
Abstract
We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. At the same time we obtain a new lower bound on the tensor rank of tensor powers of the generalised W-state tensor. In addition, we exactly determine the tensor rank of the tensor cube of the three-party W-state tensor, thus answering a question of Chen et al.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jeroen Zuiddam,