矩阵广义对角占优性的判定

Criteria of the Generalized Diagonally Dominant Matrices

利用线性方程组解的理论得到了矩阵广义对角占优的又一判定定理 ,对于用此方法判定的广义对角占优矩阵A ,可具体给出正对角阵Λ ,使AΛ为对角占优阵。作为应用还得到了矩阵非奇异的判定定理。最后给出了应用实例。

This paper presents a sufficient condition for generalized diagonally dominant matrices by using the theory of the system of linear equations.For a generalized diagonally dominant matrix A ,a positive diagonally matrix Λ ,can be given to make A Λ a diagonally dominant matrix.Some criteria for nonsingular matrices are also obtained and practical examples given.