徐常青.完全正矩阵的整数分解[J].数学研究及应用,2003,23(2):349~354
完全正矩阵的整数分解
Factorizations of Completely Positive Matrices over Integers
投稿时间:2000-05-15  
DOI:10.3770/j.issn:1000-341X.2003.02.029
中文关键词:  矩阵  完全正  整数分解
英文关键词:matrix  completely positive  factorization over integers  factorization index
基金项目:安徽省自然科学基金资助项目(010460101)
作者单位
徐常青 安徽大学数学系,安徽,合肥,230039 
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中文摘要:
      n阶矩阵A称为完全正的,如果A有分解:A=BBT,其中B为元素非负矩阵,B的最小可能列数称为A的分解指数.本文考察低阶双非负矩阵在整数环上的完全正分解及其分解指数.
英文摘要:
      An n×n matrix A is said to be completely positive if A can be factored as A = BBT, where B is an n×m nonnegative matrix. The smallest such number m is called the factorization index of A; A is called doubly nonnegative if it is entrywise nonnegative and positive semidefinite as well. The paper concerns completely positive factorizations of matrices (with integeral entries) in CP, over integers and the related factorization index.
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