摘要
本文证明了广义对角占优矩阵A当对角线元素皆为实数时,A的特征值实部为正负的个数与对角元素α_(ij)(j=1,2,…,n)中正负数的个数相同,使得文献[4]的结果成为本文的一个特例。还得到了关于准广义对角占优矩阵和共轭广义对角占优矩阵的相应结论。同时对对角元素为复数和纯虚数的情况进行了探讨。本文得到的一些结论在微分方程的稳定性理论中有重要应用。
Generalized diagonal dominance matrix A is proved in thispaper, when the elements of diagonal are all real numbers, the number ofpositive and negative for the matrix A's real part of the characteristicsare equal to that of diagonal elements A_(jj)(j=1, 2, …, n). This make resultof Ref [4] become aispeeial case of this paper. Furthermore acorrespondingconclusion is gainned, that is quasigeneralized diagonal dominance matrixand con juate generalized diagonal dominance matrix. Meanwhile we discussthe diagonal clements which are complex number and pure imaginery number some conclusion gainned from this paper play an important part inthe theory of stoility of differentiate equation.
关键词
矩阵
特征值
对角
Matrix
Characteristics
