有关完全正定阵的综述

A survey on completely positive matrices

对于给定的一个n阶实方阵A,若其每一元素非负且半正定,则称为双非负矩阵.称A为完全正定阵,如果能表示成A=BB′,其中B=(bij)n×m是非负阵,m为某一正整数,B的可能最小的列数m称为A的因子分解指数。本文综合在这方面的研究进展,其中包含作者本人有关完全正定阵的一些最新结果.

A doubly nonnegative matrix A is defined to be an entrywise nonnegative and positive semidefined matrix. It is called completely positive if it can be factored as A=BB′, where B is n×m entrywise nonnegative matrix and m is some positive integer. Such number m is called the cprank (or the factorization index) of A. The present paper gives a survey of the development in this research field . Some recent results concerning complete positivity are included.