| 关于完全正矩阵的非负分解 |
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| 引用本文： | 徐常青,李世航.关于完全正矩阵的非负分解[J].安徽大学学报(自然科学版),1999,23(1):6-10. |
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| 作者姓名： | 徐常青 李世航 |
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| 作者单位： | 安徽大学数学系,合肥,230039 |
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| 摘 要： | Ｎ阶矩阵Ａ称为完全正的，如果Ａ能分解成Ａ＝ｂ１ｂｔ１＋…＋ｂｍｂｔｍ，其中ｂｊ（ｊ＝１，２，…，ｍ）为ｎ维非负向量。满足此式的最小的正整数ｍ称为Ａ的分解指数。本文证明了一个秩≤２的非负半正定矩阵一定为完全正，并给出了一个秩为３的非负半正定矩阵为完全正的一个充分条件。
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| 关 键 词： | 双非负矩阵，完全正矩阵，分解指数 |
On Nonnegative Factorizations of Completely Positive Matrices |
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| Xu Changqing,Li Shihang.On Nonnegative Factorizations of Completely Positive Matrices[J].Journal of Anhui University(Natural Sciences),1999,23(1):6-10. |
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| Authors: | Xu Changqing Li Shihang |
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| Institution: | Department of Mathematics Anhui University Hefei 230039 |
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| Abstract: | An n×n matrix A is called completely positive if A can be factored as A=b 1b t 1+…+b mb t m. Here b j(j=1,2,…,m) are nonnegative vectors in R n .The least such integer m is called the factorization index (or CP rank) of A. It is shown that a doubly nonnegative matrix A with rank (A)≤2 is always completely positive. And a sufficient condition for a doubly nonnegative matrix with its rank equals 3 to be completely positive is presented here. |
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| Keywords: | doubly nonnegative matrix completely positive matrix factorization index |
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