方阵乘幂的一种计算方法

计算方阵的乘幂有许多不同方法，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上，还是在计算上都没有成熟。为此，本文仅借助常系数齐次线性差分方程组和哈密顿．凯莱定理出发，推出了计算方阵乘幂的一种新方法。

The Unusual Calculation Method on the Power of a Square Matrix

There are many different methods to calculate the power of a square matrix such as mathematical induction, binomial method, the standard form of Jordan law, matrix decomposition as well as splitting methods, but 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.