| 一阶常系数线性齐次微分方程组的两种解法 |
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| 引用本文： | 吴翠兰,乔文敏. 一阶常系数线性齐次微分方程组的两种解法[J]. 石家庄经济学院学报, 1995, 0(5) |
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| 作者姓名： | 吴翠兰 乔文敏 |
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| 作者单位： | 河北地质学院基础课部 石家庄050031 |
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| 摘 要： | 一阶常系数线性齐次微分方程组其中的求解,一般有两种解法。第一种,归结为求矩阵A的特征值和特征向量,微分方程组(1)的解的一般结构完全由代数问题的解所决定。第二种,归结为求矩阵A的Jordan标准形,从而可以写出,由其中为可逆矩阵,求出即为方程组(1)的解。
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| 关 键 词： | 矩阵解 特征值 特征向量 Jordan标准形 |
Two Solutions of the First-Order Homogeneous Linear Differential Equation Group |
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| Wu Cuilan Qian Wenmin. Two Solutions of the First-Order Homogeneous Linear Differential Equation Group[J]. Journal of Shijiazhuang University of Economics, 1995, 0(5) |
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| Authors: | Wu Cuilan Qian Wenmin |
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| Abstract: | This paper is about the solutions of the first -order homogeneous linear differential e-quation groups x (t) =Ax(t)(1),A=(aij),x=(x1,x2,xn)T.The author introduces two different solutions. The first one can be concluded to get the eigenvalues and eigenvectors e-quation groups,because the general structure of the solution of the differential equation group (1) is determined totally by the solution of algebra equation. The second one is to seek the JordanCanonical form of Matrix A;write out y1,y2;yn;getX= P-1 y where y =and finallyobtain x=which is the solution of equation group (1). |
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| Keywords: | matrix solution eigenvalue eigenvector Jordan canonical form |
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