期刊文献+

COMPLETELY POSITIVE MATRICES OF ORDER FIVE

COMPLETELY POSITIVE MATRICES OF ORDER FIVE
全文增补中
导出
摘要 A real matrix A of order n is called doubly nonnegative (denoting A∈DPn) if it is non- negative entrywise and positive semidefinite as well. A is called completely positive (denoting A∈CPn) if there exist k nonnegative column vectors b1,b2, …,bk∈Rn for some nonnegative integer k such that A=b1b′1+…+bkb′k. The smallest such number k is called the factorization index of A and is denoted by φ(A). This paper gives an effective criterion for any doubly nonnegative matrix A of order 5 whose associated graph is isomorphic neither to K5(the complete graph) nor to K5-e (a subgraph of K5 obtained by cutting off an edge from it) to be completely positive. A real matrix A of order n is called doubly nonnegative (denoting A∈DPn) if it is non- negative entrywise and positive semidefinite as well. A is called completely positive (denoting A∈CPn) if there exist k nonnegative column vectors b1,b2, …,bk∈Rn for some nonnegative integer k such that A=b1b′1+…+bkb′k. The smallest such number k is called the factorization index of A and is denoted by φ(A). This paper gives an effective criterion for any doubly nonnegative matrix A of order 5 whose associated graph is isomorphic neither to K5(the complete graph) nor to K5-e (a subgraph of K5 obtained by cutting off an edge from it) to be completely positive.
作者 徐常青
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第4期550-562,共13页 应用数学学报(英文版)
基金 the fund of Anhui Education Committee.
关键词 Doubly nonnegative matrix completely positive matrix factorization index Doubly nonnegative matrix, completely positive matrix, factorization index
  • 相关文献

参考文献1

  • 1XU Changqing (Department of Mathematics, Anhui University, Hefei 230039, China) LI Jiongsheng (Department of Mathematics, University of Science and Technology of China, Hefei 230026, China).A NOTE ON COMPLETELY POSITIVE GRAPHS[J].Systems Science and Mathematical Sciences,2000,13(2):121-125. 被引量:3

共引文献2

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部