Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 28, Issue 3, Pages 642-666Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040608830
Keywords
multilinear algebra; higher-order tensor; canonical decomposition; parallel factors model; simultaneous matrix diagonalization
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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.
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