DECOMPOSITIONS OF A HIGHER-ORDER TENSOR IN BLOCK TERMS-PART I: LEMMAS FOR PARTITIONED MATRICES
DECOMPOSITIONS OF A HIGHER-ORDER TENSOR IN BLOCK TERMS-PART I: LEMMAS FOR PARTITIONED MATRICES
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DOI：
10.1137/060661685
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发表时间：
2008-01-01
影响因子：
1.5
通讯作者：
De Lathauwer, Lieven
中科院分区：
文献类型：
--
作者：
De Lathauwer, Lieven
在本文中，我们研究了克鲁斯卡尔置换引理对划分矩阵的推广。我们将划分矩阵的 k' 秩定义为矩阵 k 秩的推广。我们推导出划分矩阵的 Khatri-Rao 乘积的 k' 阶下界。我们证明分区矩阵的 Khatri-Rao 乘积通常是满列秩的。
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.