Ranks of tensors and a generalization of secant varieties
Algebraic Geometry
2014-06-02 v5
Abstract
We introduce subspace rank as a tool for studying ranks of tensors and X-rank more generally. We derive a new upper bound for the rank of a tensor and determine the ranks of partially symmetric tensors in C^2 \otimes C^b \otimes C^b. We review the literature from a geometric perspective.
Cite
@article{arxiv.0909.4262,
title = {Ranks of tensors and a generalization of secant varieties},
author = {Jarosław Buczyński and J. M. Landsberg},
journal= {arXiv preprint arXiv:0909.4262},
year = {2014}
}
Comments
22 pages; final published version; Linear Algebra and its Applications 2012