On Kruskal's uniqueness condition for the Candecomp/Parafac decomposition
The Candecomp/Parafac-decomposition of the real valued three-way array \(X\) is written as \(X=\underline{Y}^{(1)} + \ldots + \underline{Y}^{(R)} +\underline{E}\), where \(\underline{Y}^{(r)}\) are rank one arrays defined as outer products of three specified vectors and \(\underline E\) is a rest term. The question of uniqueness for this decomposition is provided by the theorem of \textit{J. B. Kruskal} [Linear Algebra Appl. 18, 95-138 (1977; Zbl 0364.15021)]. The authors obtain an accessible and more simple proof of Kruskal theorem, which can be easily adopted to the complex case.
scientific article; zbMATH DE number 5083623