摘要
计算方阵的乘幂有许多种不同方法.如数学归纳法、二项式法、Jordan标准型法和拆分法等.这些方法无论在理论还是计算上,没有一个是完全令人满意的.为此,本文仅借助常系数齐次线性差分方程组和哈密顿——凯莱定理这两个知识点,得出了一种计算方阵乘幂的新方法。
There are many different methods to calculate the power of a square matrix: mathematical induction,binomial method,the standard form of Jordan law,matrix decomposition,and splitting methods,none of which is entirely satisfactory from either a theoretical or a computational point of view. In this paper an elementary method of calculating any power of a given square matrix is described that uses the students’ knowledge of homogeneous linear difference equations with constant coefficients and the Hamilton- Cayley theorem.
出处
《内蒙古农业大学学报(自然科学版)》
CAS
北大核心
2014年第4期153-156,共4页
Journal of Inner Mongolia Agricultural University(Natural Science Edition)
基金
新疆维吾尔自治区高校科研计划重点项目(项目编号:XJEDU2008Ⅰ31)
关键词
矩阵代数
常系数
线性差分方程组
初值问题的解
特征多项式
matrix algebra
constant coefficients
linear difference equations
the solution of initial value problem
characteristic polynomial