Kruskal's uniqueness inequality is sharp
type: Item
instance of: scholarly article
title: Kruskal's uniqueness inequality is sharp
zbMATH Open document ID: 1267.15022
published in: Linear Algebra and its Applications
publication date: 2013-01-16T00:00:00Z
review text: Let \(F\) be a field and \(V\) an \(F\)-vector space. For a subset \(A\subset V\), the Kruskal rank \(k(A)\) is the largest integer such that \(A\) has at least \(k(A)\) elements and every subset of \(A\) with \(k(A)\) elements is linearly independent. For \(m\) vector spaces \(V_1,V_2,\dots,V_m\) over \(F\), \textit{J. B. Kruskal} [Linear Algebra Appl. 18, 95--138 (1977; Zbl 0364.15021)] proved that a tensor in \(V_1\otimes V_2\otimes \dots\otimes V_m\) of rank \(r\) has a unique decomposition as a sum of \(r\) pure tensors if a certain inequality is satisfied. The author of the paper shows that the uniqueness fails if the inequality is weakened.
reviewed by: Manouchehr Misaghian
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 6125886
zbMATH Keywords: tensors
zbMATH Keywords: multi-way arrays
zbMATH Keywords: Kruskal's theorem
zbMATH Keywords: Kruskal rank
zbMATH Keywords: inequality
author: Harm Derksen
MaRDI profile type: Publication
full work available at URL: j.laa.2011.05.041
OpenAlex ID: W2008751154
cites work: Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
cites work: A concise proof of Kruskal's theorem on tensor decomposition
cites work: On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
DOI: 10.1016/J.LAA.2011.05.041
description: scientific article; zbMATH DE number 6125886