| 关于常系数齐次线性微分方程组的解法研究 |
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| 引用本文： | 杨彩琴.关于常系数齐次线性微分方程组的解法研究[J].数学学习,2010,13(3):21-23. |
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| 作者姓名： | 杨彩琴 |
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| 作者单位： | 内蒙古农业大学理学院,呼和浩特,010018 |
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| 摘 要： | 利用凯莱-哈密顿定理给出矩阵指数函数eAt的简洁计算方法;同时利用约当标准形推导出求常系数齐次线性微分方程组通解的循环公式.
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| 关 键 词： | 常系数齐次线性微分方程组 矩阵指数函数 约当标准形 循环公式 |
Solving Homogeneous LDE Systems with Constant Coefficients |
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| YANG Cai Qin.Solving Homogeneous LDE Systems with Constant Coefficients[J].Studies In College Mathematics,2010,13(3):21-23. |
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| Authors: | YANG Cai Qin |
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| Institution: | (School of Science, Inner Mongolia Agricultural University, Hohhot, 10018, PRC) |
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| Abstract: | This paper presents a succinct algorithm, using the Cayley-Hamilton theorem, for e^At, the exponential function of a matrix A. This paper also uses Jordan Forms to derive a recursive formula for the general solution of the system of homogeneous linear ordinary differential equations with constant coefficients. |
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| Keywords: | Systems of homogeneous linear differential equations with constant coefficient matrix index function Jordan normal form circular formula |
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