| 关于圈的完全正矩阵实现 |
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| 引用本文： | 徐常青. 关于圈的完全正矩阵实现[J]. 数学研究及应用, 2002, 22(3): 391-395 |
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| 作者姓名： | 徐常青 |
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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： | Supported by Anhui Edncation Committee(LJ990007) |
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| 摘 要： | 本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.
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| 关 键 词： | 圈 完全正矩阵 关联图 |
| 收稿时间： | 1999-05-11 |
Completely Positive Realizations of a Cycle |
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| XU Chang-qing. Completely Positive Realizations of a Cycle[J]. Journal of Mathematical Research with Applications, 2002, 22(3): 391-395 |
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| Authors: | XU Chang-qing |
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| Affiliation: | Dept. of Math.; Auhui University; Hefei; China |
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| Abstract: | An n × n real matrix A is called doubly nounegative, if A is entrywise nonnegative and semidefmite positive as well. A is called completely positive if A can be factored as A=BBt,where B is some nonnegative n × m matrix. The smallest such number m is called the factorization index (or CP-rank) of A. This paper presents a criteria for a doubly nonnegative matrix realization of a cycle to be completely positive, which is strightforward and effective. |
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| Keywords: | doubly nonnegative matrix completely positive graph cycle factorization index. |
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