DECOMPOSITIONS OF A HIGHER-ORDER TENSOR IN BLOCK TERMS-PART I: LEMMAS FOR PARTITIONED MATRICES

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.