| 徐常青.关于圈的完全正矩阵实现(英文)[J].数学研究及应用,2002,22(3):391~395 |
| 关于圈的完全正矩阵实现(英文) |
| Completely Positive Realizations of a Cycle |
| 投稿时间：1999-05-11 |
| DOI：10.3770/j.issn:1000-341X.2002.03.012 |
| 中文关键词: |
| 英文关键词:doubly nonnegative matrix completely positive graph cycle factorization index. |
| 基金项目: |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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