用最小多项式求线性微分方程组的基解矩阵

A Method for Calculating Basic Solution Matrix of Linear Simultaneous Equations by Using Minimal Polynomial

给出了最小多项式的两个性质；从理论上阐述了最小多项式与任何由矩阵级数定义的矩阵函数间的关系，并给出了用最小多项式代替特征多项式计算矩阵函数的方法；最后通过实例验证了该方法在简化计算方面的有效性．

This paper gives the two qualities of the minimal polynomial. It expounds the relations between the minimal polynomial and any matrix function defined by matrix series in theory. It also proposes a method for calculating matrix function, with which the characteristic polynomial is substituted by the minimal polynomial. Then, the service quality of this method on simplifying calculating is demonstrated by an example.