广义严格对角占优矩阵与非奇异M-矩阵的判定  

Criteria for Generalized Strictly Diagonally Matrices and Nonsingular M-Matrices

作　　者：孙玉祥[1] 吕洪斌[1] 

机构地区：[1]北华大学,吉林吉林132013

出　　处：《厦门大学学报（自然科学版）》2001年第5期1011-1016,共6页Journal of Xiamen University：Natural Science

摘　　要：设 A =(aij)∈ Cn× n是复矩阵 ,若任意 i∈ N ={ 1,2 ,… ,n}都有 | aii| >∑j≠ i| aij| ,则称 A是严格对角占优矩阵 .若存在正对角阵 D使是 AD严格对角占优矩阵 ,则称为广义严格对角占优矩阵 .本文利用矩阵回路给出了广义严格对角占优矩阵与非奇异 M矩阵的若干充分条件 .Let A=(a ij )∈C n×n be an complex matrix, any i∈N={1,2,...,n} have |a ii |>∑j≠i|a ij |, then A is a diagonally dominant matrix. If there exists a positive diagonal matrix D such that AD is a strifctly diagonally dominant matrix, A is a generalized diagonally dominant matrix. Some sufficient conditions for a matrix to be a generalized strictly diagonally dominant matrix and some criteria for nonsingular M matrices are obtained. These results improve and generalize the known results.

关 键 词：广义严格对角占优矩阵 非奇异M-矩阵 正对角阵 矩阵回路 判定方法 

分 类 号：O151.21[理学—数学]