| 关于完全正矩阵分解指数的注记 |
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| 引用本文： | 徐常青,吴秋月.关于完全正矩阵分解指数的注记[J].安徽大学学报(自然科学版),2002,26(3):10-14. |
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| 作者姓名： | 徐常青 吴秋月 |
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| 作者单位： | 安徽大学,数学系,安徽,合肥,230039 |
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| 基金项目： | 安徽省自然科学基金;01046101; |
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| 摘 要： | 一个n×n阶的元素非负矩阵A称为双非负的,若A还是半正定矩阵,A称为完全正矩阵,如果A可以分解成 A=BB′,其中矩阵B为某个非负的n×m矩阵,m为某个自然数.这种所有可能的最小的自然数m称为矩阵A的分解指数(或称为A的CP-秩).1994年,Drew,Johnson 以及Loewy等人提出著名的DJL-猜想:对于任意一个n阶完全正矩阵A,有:CP-rank(A)≤(n2)/(4)].本文证明了在n=5以及n=6时的特殊情形下此猜想成立.
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| 关 键 词： | 完全正 双非负 分解指数 |
A note on completely positive factorization index |
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| Abstract.A note on completely positive factorization index[J].Journal of Anhui University(Natural Sciences),2002,26(3):10-14. |
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| Authors: | Abstract |
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| Abstract: | An n×n entrywise nonnegative matrix A is called doubly nonnegative if A is positive semidefinite as well;A is called completely positive if A can be factorized as A=BB′, where B is an n by m entrywise nonnegative matrix. The smallest such number m is called the factorization index (or Cprank)of A.In 1994,Drew, Johnson and Loewy conjectured that the factorization index(CPrank)of every completely positive matrix of order nis not larger than n2/4].In this paper, we prove the conjecture for some special cases for n=5 and n=6. |
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| Keywords: | completely positive matrix doubly nonnegative matrix factorization Index |
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