N阶矩阵高次幂的求法及应用.doc

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本科毕业论文
N阶矩阵m次方幂的求法及应用
Solution and Application of m-order of nn Martix
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摘 要
矩阵是许多实际问题中抽象出来的一个概念，它是高等代数的一个重要组成部分，它几乎贯穿于高等代数的各个章节，，所以，，它是以矩阵的乘法运算为基础；然而，矩阵的幂运算是比较复杂同时也是特别麻烦的，所以寻找简单的运算方法就成了计算矩阵高次幂方面的重要环节，为此很多学者都花了很大的精力去探讨研究，本文将在他们的研究基础上，应用实例通过数学归纳法，乘法结合律的方法，二项式展开式的方法，分块对角矩阵的方法，标准形法，最小多项式的方法和特殊矩阵法等多种方法来求解方阵的高次幂，进而为阶矩阵的幂运算来提供一个参考.
关键词:数学归纳法;二项展开式;矩阵的幂;相似矩阵.
Abstract
Matrix is a concept many practical problems in the abstract, it is an important part of the linear algebra, it is almost throughout the various sections of linear algebra, in the field of natural sciences and economic management of the branch has a wide range of applications. Just because it wide range of applications and is a powerful tool for solving many problems, so learn and master the operation and their method of operation rules and good matrix is a matrix of knowledge we learn a very important part. For matrix power calculations, it is Matrix multiplication is based; however, the matrix exponential operation is more complex but also particularly troublesome, so look for a simple calculation method has become an important part of computing power matrix high regard, for many scholars have spent a lot of research effort to investigate, the paper will be on the basis of their research, application examples by mathematical induction, multiplication associative approach, binomial expansion method, the method block diagonal matrix, standard form method, minimal polynomial a variety of methods and special methods to solve the matrix method phalanx of high-power, and thus the power to order matrix operations to provide a refere