广义严格对角占优矩阵的充分必要条件

The necessary and sufficient conditions of generalized strictly diagonally dominant matrix

非奇异广义严格对角占优矩阵是实际背景很广的一类矩阵,它在控制论、电子系统理论、经济数学以及弹性力学等领域都有广泛的应用。它与M矩阵及正定矩阵都有特殊的关系。本文给出了判定广义严格对角占优矩阵的几个充分必要条件。广义对角占优矩阵是计算数学和矩阵理论研究的重要课题之一。本文中改进了近期一些结果,对广义严格对角占优矩阵的判定问题进行了进一步的推广。

The non singular generalized strictly diagonally dominant matrix is a category of matrix with broad actual context,which has broad application in the control theory,system theory,mathematical economics and electron elastic mechanics and other fields.It has a special relationship with M matrices and positive definite matrix.This paper presents several necessary and sufficient conditions of the determination conditions of generalized strictly diagonally dominant matrix and.Generalized diagonally dominant matrix is one of the important research topics of the mathematical calculation and matrix theory.In this paper,some recent results are improved,the criteria for generalized strictly diagonally dominant matrix problems are further promoted.