关于完全正矩阵分解指数的注记(英文)  

A note on completely positive factorization index

作　　者：徐常青[1] 吴秋月[1] 

机构地区：[1]安徽大学数学系,安徽合肥230039

出　　处：《安徽大学学报（自然科学版）》2002年第3期10-14,共5页Journal of Anhui University(Natural Science Edition)

基　　金：SupportedbyNSFofAnhuiProvince(0 1 0 4 61 0 1 )

摘　　要：一个n×n阶的元素非负矩阵A称为双非负的 ,若A还是半正定矩阵 ,A称为完全正矩阵 ,如果A可以分解成A =BB′,其中矩阵B为某个非负的n×m矩阵 ,m为某个自然数。这种所有可能的最小的自然数m称为矩阵A的分解指数 (或称为A的CP -秩 )。 1 994年 ,Drew ,Johnson以及Loewy等人提出著名的DJL -猜想 :对于任意一个n阶完全正矩阵A ,有 :CP -rank(A) ≤ [n24 ] .本文证明了在n=5以及n=6时的特殊情形下此猜想成立。An n×n entrywise nonnegative matrix A is called doubly nonnegative if A is positive semidefinite as well;A is called completely positive if A can be factorized as A=BB′ , where B is an n by m entrywise nonnegative matrix. The smallest such number m is called the factorization index (or Cprank)of A .In 1994,Drew, Johnson and Loewy conjectured that the factorization index(CPrank)of every completely positive matrix of order n is not larger than .In this paper, we prove the conjecture for some special cases for n=5 and n=6.

关 键 词：完全正矩阵 双非负 分解指数 半正定矩阵 非负矩阵 DJL-猜想 

分 类 号：O151.21[理学—数学]