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关于逆M-矩阵Hadamard积的一个猜想

ZHOU Yu-zhong,FANG Ping,ZHANG Xin

Journal of Jiangxi Normal University(Natural Sciences Edition)（2008）

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Abstract
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.
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Key words
Ultrametric matrices,inverse M-matrix,M-matrix,Willongby inverse M-matrices.,Hadamard product
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