应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2012年
4期
433-436
,共4页
Hadamard积%M-矩阵%逆M-矩阵%P-矩阵
Hadamard積%M-矩陣%逆M-矩陣%P-矩陣
Hadamard적%M-구진%역M-구진%P-구진
Hadamard product%M-matrix%inverse M-matrix%P-matrix
A=[aij]∈Mn和B=[bij]∈Mn的Hadamard积可表示为AοB = [aijbij]∈Mn. 如果A, B ∈Mn是M-矩阵, 那么AοB-1也是M-矩阵. 证明了（a）一个非奇异的M-矩阵是一对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.
A=[aij]∈Mn和B=[bij]∈Mn的Hadamard積可錶示為AοB = [aijbij]∈Mn. 如果A, B ∈Mn是M-矩陣, 那麽AοB-1也是M-矩陣. 證明瞭（a）一箇非奇異的M-矩陣是一對M-矩陣和逆M-矩陣的Hadamard積, 同時也證明瞭（b）一箇P-矩陣是兩箇P-矩陣的Hadamard積.
A=[aij]∈Mn화B=[bij]∈Mn적Hadamard적가표시위AοB = [aijbij]∈Mn. 여과A, B ∈Mn시M-구진, 나요AοB-1야시M-구진. 증명료（a）일개비기이적M-구진시일대M-구진화역M-구진적Hadamard적, 동시야증명료（b）일개P-구진시량개P-구진적Hadamard적.
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.
