Completely positive matrices

被引：11
|
作者：
Xu, CQ [1 ]
机构：
[1] Anhui Univ, Dept Math, Hefei 230039, Peoples R China
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 379卷
关键词：
completely positive matrix; doubly nonnegative matrix; factorization;
D O I：
10.1016/S0024-3795(03)00611-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An n x n real matrix A is called completely positive (CP) if it can be factored as A = B' B ("/" stands for transpose) where B is an m x n entrywise nonnegative matrix for some integer in. The smallest such number in is called the cprank of A. In this paper we present a necessary and sufficient condition for any entrywise nonnegative and positive semidefinite matrix to be CP. We also present an expression for the cprank of any CP matrix. (C) 2003 Elsevier Inc. All rights reserved.
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页码：319 / 327
页数：9
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