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

Authors:
Lieven De Lathauwer
Affiliations:
Lieven.DeLathauwer@kuleuven-kortrijk.be
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2008

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Abstract

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.