Ranks of tensors and a generalization of secant varieties

By Jaroslaw Buczy'nski, J. M. Landsberg. 2009

95 citations recorded by the source corpus.

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 ⊗ C b ⊗ C b . We review the literature from a geometric perspective.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/87685523fd75405e15d632a84477159d514fbf41

Citations in the corpus

• Zur Theorie der Niedrigrangapproximation in Tensorprodukten von Hilberträumen (2013, unknown): “Landsberg [15] beweisen rmax(n,n,n) ≤ n2−n−1 für K=C.”