关于逆M-矩阵Hadamard积的一个猜想

A Conjecture Concerning the Hadamard Product of Inverse MMatrices

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.