零化多项式的一个应用

The Application of Zeroized Polynomial

利用矩阵的零化多项式 ,给出计算标准基解矩阵 e At的一个公式 .利用向量关于矩阵的零化多项式 ,给出常系数齐次线性微分方程组初值问题的一个求解公式 .相应地 ,可以推出常系数齐次线性差分方程组在给定的初始条件下的一个求解公式 .

Using matrix-zeroized polynomial, the formula for calculating standard fundamental solution matrix e At, is given. Appling zeroized polynomial of matrix with vector,another formula for solving the initial value system of linear differential equation whith constant coefficients, is obtained. So, a formula to solve the homogeneous linear differential equations with constant coefficients under certain initial conditions can be derived.