常系数线性方程组基解矩阵的计算

下载后可任意编辑常系数线性方程组基解矩阵的计算董治军（巢湖学院 数学系，安徽 巢湖 238000）摘 要：微分方程组在工程技术中的应用时非常广泛的，不少问题都归结于它的求解问题，基解矩阵的存在和具体寻求是不同的两回事，一般齐次线性微分方程组的基解矩阵是无法通过积分得到的，但当系数矩阵是常数矩阵时，可以通过 方法求出基解矩阵，这时可利用矩阵指数t，给出基解矩阵的一般形式，本文针对应用最广泛的常系数线性微分方程组，结合微分方程，线性代数等知识，讨论常系数齐次线性微分方程的基解矩阵的几个一般的计算方法.关键词；常系数奇次线性微分方程组；基解矩阵；矩阵指数Calculation of Basic solution Matrix of Linear Homogeneous System with Constant CoefficientsZhijun Dong(Department of Mathematics, Chaohu College Anhui, Chaohu)Abstract: Differential equations application in engineering technology is very extensive, when many problems are attributable to its solving problem, base solution matrix existence and specific seek is different things, general homogeneous linear differential equations is not the base solution matrix by integral get, but when coefficient matrix is constant matrix, can pass out the base solution matrix method, then are available matrix exponential t, the general form base solution matrix, the paper discusses the most widely used differential equations with constant coefficients, combined with differential equations, linear algebra, discuss knowledge of homogeneous linear differential equation with constant coefficients of base solution matrix several general calculation method.Keyword: linear homogeneous system with constant coefficients; matrix of basic solutions; matrix exponent引言:线性微分方程组的求解历来是常微分方程的重点，根据线性微分方程组的解的结构理论，求解线性微分方程组的关键在于求出对应齐次线性微分方程组的基解矩阵，本文主要讨论齐次线性微分方程组 X’＝AX ★ 的基解矩阵的计算问题，这里A 是常数矩阵.一．矩阵指数的定义和性质：1.矩...