关于逆M-矩阵Hadamard积的一个猜想  

A Conjecture Concerning the Hadamard Product of Inverse MMatrices

作　　者：周裕中[1] 方平[1] 张昕[1] 

机构地区：[1]华南农业大学理学院数学系,广东广州510640

出　　处：《江西师范大学学报（自然科学版）》2008年第4期399-402,共4页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(10726070,60663002);华南农业大学校长基金(2007K023)资助项目

摘　　要：对一个n×n逆M-矩阵A,M.Neumann猜想其Hadamard积■ A也是逆M-矩阵.通过许多例子验证,它们都是正确的.迄今为止,猜想未被证出.该文研究了该猜想,给出了一类不同的逆M-矩阵,验证Hadamard积■ A与■ B都是封闭的.进一步验证了猜想:当p≥1,A及任意Ai(i=1,2,…,N-1,N)是逆M-矩阵时,Hadamard幂■ p=(aipj),■∞=(aij∞),Hadamard积■■…oAN都是封闭的.For an n×n matrix A which is an inverse M-matrix,M.Neumann conjectured that the Hadamard product ■ A is an inverse of M-matrix.They have checked the conjecture without failure on many examples.So far,the conjecture has not been proved.In the paper,we study the conjecture.We present a different class inverse M-matrix and investigate the Hadamard product ■ A and ■ B are closed.We also check a more general conjecture that for any p≥1,the Hadamard power ■ p=(apij),■ ∞=(a∞ij) and the Hadamard multiplication ■ ■ ■…o AN are closed when A and any Ai(i=1,2,…,N-1,N) are inverse M-matrices.

关 键 词：M-矩阵 逆M-矩阵 HADAMARD积 Ultrametric矩阵 Willongby逆M-矩阵 

分 类 号：O151.21[理学—数学]