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arXiv · 0909.4262

Ranks of tensors and a generalization of secant varieties

Jarosław Buczyński·J. M. Landsberg
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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.

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Jarosław Buczyński, J. M. Landsberg. 2009-09-23. Ranks of tensors and a generalization of secant varieties. https://doi.org/10.1016/j.laa.2012.05.001

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