A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization

@article{Lathauwer2006ALB,
  title={A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization},
  author={L. Lathauwer},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2006},
  volume={28},
  pages={642-666}
}
  • L. Lathauwer
  • Published 2006
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 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… CONTINUE READING
    357 Citations

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