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.
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.
基金
安徽省自然科学基金资助项目(010460101)
关键词
完全正矩阵
整数分解
分解指数
完全正分解
matrix
completely positive
factorization over integers
factorization index
