M-矩阵和逆M-矩阵的Hadamard积(英文)  

On Hadamard product of M-matrices and inverse M-matrices

作　　者：方茂中[1] 张寄洲[2] 

机构地区：[1]上海立信会计学院数学与信息学院,上海201620 [2]上海师范大学数理学院,上海200234

出　　处：《应用数学与计算数学学报》2012年第4期433-436,共4页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Foundation of China(11201304,11178014);the Science Foundation of Shanghai Municipal Education Commission(13ZZ107)

摘　　要：A=[a_(ij)]∈M_n和B=[b_(ij(]∈M_n的Hadamard积可表示为AoB=[a_(ij)b_(ij)]∈M_n.如果A,B∈M_n是M-矩阵,那么AoB^(-1)也是M-矩阵.证明了(a)一个非奇异的M-matrix是一对M-矩阵和逆M-矩阵的Hadamard积,同时也证明了(b)一个P-矩阵是两个P-矩阵的Hadamard积.The Hadamard product of A=[aij]∈Mn and B=[bij]∈Mn is denoted by AοB = [aijbij]∈Mn. If A, B ∈Mn are M-matrices, then so is AοB-1. It is shown that （a） a nonsingular M-matrix is the Hadamard product of a nonsingular M-matrix and an inverse M-matrix, and （b） a P-matrix is a Hadamard product of two P-matrices.

关 键 词：HADAMARD积 M-矩阵 逆M-矩阵 P-矩阵 

分 类 号：O151.21[理学—数学]