广义严格对角占优矩阵与非奇M矩阵的充要条件

Necessary and sufficient conditions of generalized strictly diagonally dominant matrices and nonsingular M-matrices

广义严格对角占优矩阵与非奇 M矩阵是非常重要的两类矩阵。文章给出了实方阵为广义严格对角占优矩阵和实方阵的比较矩阵为非奇 M矩阵的充要条件。同时 ,给出了判别广义严格对角占优矩阵 (非奇 M矩阵 )简单实用的方法 ,该方法只需要解一个非齐次线性方程组即可。

Generalized strictly diagonally dominant matrices and nonsingular M-matrices are two kinds of important matrices. In this paper the necessary and sufficient (NS) condition of real square matrix(RSM) to be a generalized strictly diagonally dominant matrix and the NS condition of the RSM′s comparison matrix to be a nonsingular M-matrix are given.A simple and practicable method of judging generalized strictly diagonally dominant matrices and nonsingular M-matrices is introduced. When this method is adopted,only a non-homogeneous linear equation is needed to solve.