矩阵在常系数线性递推关系中的应用

矩阵在常系数线性递推关系中的应用(论文5400字)
【内容摘要】  本文在前人的研究基础上，对应用矩阵的相关知识与常系数线性递推关系进行研究.首先，归纳出一些矩阵的相关知识.其次，应用矩阵来表示常系数线性递推关系.然后再应用矩阵求解常系数线性递推关系，介绍矩阵方法如何应用.最后，举出简单的递推关系的问题，用一般方法和矩阵方法分别对这些问题进行解答，并比较这些方法在解决实际问题中的优劣之处，提出一些自己的建议.将递推关系组与矩阵相结合，用矩阵对角化及特征值理论求解一类递推关系组，并给出通解.
【关键词】  矩阵的加法；可对角化；应用矩阵；递推关系；

Application of Matrix in Linear Recursive relation with constant coefficients
[Abstract]  On the basis of previous studies, this paper studies the relationship between the relative knowledge of applied matrices and linear recursion of constant coefficients. Firstly, some related knowledge of matrices is summarized. The matrix is used to express the linear recursion relation of constant coefficient, then the matrix is used to solve the linear recursive relation of constant coefficient, and how to apply the matrix method is introduced. Finally, the problem of simple recursive relation is given. The general method and matrix method are used to solve these problems, and the advantages and disadvantages of these methods in solving practical problems are compared, and some suggestions are put forward. To solve the problem of matrix diagonalization and eigenvalue theory Class recursive relation group, and give the general solution.
[Key words]  Keywords addition of matrix; diagonalization; application matrix; recursive relation

目    录
内容摘要    1
关键词    1
1引言    1
1.1研究现状    1
1.2研究意义    2
1.3研究思路及研究方法    2
2矩阵相关知识    2
2.1矩阵的加法和数与矩阵的乘法    2
2.2矩阵的乘法    3
2.3矩阵对角化    4
2.4可对角化矩阵的性质    5
3矩阵在常系数线性递推关系中的应用    7
3.1矩阵在常系数线性齐次递推关系(组)的应用    8
3.1.1应用矩阵表示常系数线性齐次递推关系    8
3.1.2矩阵方法求解常系数线性齐次递推关系    9
3.2矩阵在常系数线性非齐次递推关系(组)的应用    11
3.2.1应用矩阵表示常系数线性非齐次递推关系    11
3.2.2矩阵方法求解常系数线性非齐次递推关系    12
4应用矩阵方法求解常系数线性递推关系的优劣     13
5结论    15
参考文献    16
Abstract    16
Key words    16