A Multilinear Singular Value Decomposition

@article{Lathauwer2000AMS,
  title={A Multilinear Singular Value Decomposition},
  author={Lieven De Lathauwer and Bart De Moor and Joos Vandewalle},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2000},
  volume={21},
  pages={1253-1278}
}
We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors. 

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