Title: A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization
Abstract: Canonical decomposition is a key concept in multilinear algebra. In this paper we consider the decomposition of higher‐order tensors which have the property that the rank is smaller than the greatest dimension. We derive a new and relatively weak deterministic sufficient condition for uniqueness. The proof is constructive. It shows that the canonical components can be obtained from a simultaneous matrix diagonalization by congruence, yielding a new algorithm. From the deterministic condition we derive an easy‐to‐check dimensionality condition that guarantees generic uniqueness.
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 414
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