Decompositions of a Higher-Order Tensor in Block Terms - Part I: Lemmas for Partitioned Matrices

@article{Lathauwer2008DecompositionsOA,
  title={Decompositions of a Higher-Order Tensor in Block Terms - Part I: Lemmas for Partitioned Matrices},
  author={Lieven De Lathauwer},
  journal={SIAM J. Matrix Analysis Applications},
  year={2008},
  volume={30},
  pages={1022-1032}
}
In this paper we study a generalization of Kruskal’s permutation lemma to partitioned matrices. We define the k’-rank of partitioned matrices as a generalization of the k-rank of matrices. We derive a lower-bound on the k’-rank of Khatri–Rao products of partitioned matrices. We prove that Khatri–Rao products of partitioned matrices are generically full column rank. 
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