n阶方阵高次幂的求解方法  

The Method of Solving the Higher Power of n-order Square Matrix

作　　者：张海涛 ZHANG Hai-tao(School of Mathematics and Statistics Science,Shanxi Datong university,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2020年第1期24-26,共3页Journal of Shanxi Datong University(Natural Science Edition)

摘　　要：方阵高次幂的计算问题,掌握起来有一定的难度,用定义计算方阵的幂十分繁琐,结合实例介绍了数学归纳法、二项式展开法、矩阵分解法、对角矩阵法、哈密顿定理等几种方阵的幂的常用求解方法。It is difficult to master the calculation of high power of square matrix.It is very complicated to calculate the power of square matrix by defining.This paper introduces several common methods of solving power of square matrix,such as mathematical in⁃duction,binomial expansion,matrix decomposition,diagonal matrix method,Hamilton theorem and so on.

关 键 词：方阵 初等矩阵 数学归纳法 相似对角化 

分 类 号：O13[理学—数学]