常系数齐次线性常微分方程的解  

Solution of System of Homogeneous Linear Ordinary Differential Equations With Constant Coeffient

作　　者：王五生 

机构地区：[1]河池师专数学系,讲师广西宜州546300

出　　处：《河池师范高等专科学校学报》2000年第2期23-25,49,共4页

摘　　要：本文首先证明了若当标准形矩阵有n个线性无关的循环向量 ,接着证明了常系数齐次线性常微分方程组存在m个与它的系数矩阵的m重特征根对应的线性无关的解。最后证明了常系数齐次线性常微分方程组存在n个线性无关的解 。This paper first proves that Jordan's canonical matrix of order n has n linearly independant cyclic vector, and then proves that system of homogeneous linear ordinary differential equations with constant coeffients has m linearly independant solutions which correspond to m-ple eginvalues of the coeffient matrix. Finally it proves that system of homogeneous linear ordinary differetial equations with constant coeffients has n linearly independant solutions and arbitrary solution is linear combination of the n slutions .

关 键 词：常系数齐次线性常微分方程 若当标准形 重特征根 线性无关解 解空间 循环向量 

分 类 号：O175.1[理学—数学] O241.81[理学—基础数学]