安徽大学学报（自然科学版）2000，Vol.24Issue(4)：1-6,6.
双随机情形下的完全正矩阵
Doubly Stochastical Matrices and Complete Positivity
摘要
Abstract
A real square matrix A is called doubly nonnegative, if A is entrywise nonnegative and positive semidefinite as well; A is called completely positive, if there exists an (not necessarily square) n×m entrywise nonnegative matrix B , such that A = BB＇ . The least possible number m of columns of B is called the factorization index of A . It is known that every irreducible doubly nonnegative matrix has a doubly stochastic pattern. Therefore the complete positivity of a doubly nonnegative matrix can be reduced to the case for a doubly stochastic、positive semidefinite matrix. The paper concerns the complete positivity of doubly stochastic matrices. Also necessary and sufficient conditions for some special types of doubly stochastic matrices to be completely positive are given here.关键词
矩阵/完全正/双随机Key words
complete positivity/doubly stochastic引用本文复制引用
徐常青..双随机情形下的完全正矩阵[J].安徽大学学报（自然科学版）,2000,24(4):1-6,6.基金项目
安徽省教委基金资助项目 （）
