求任意阶递推关系通项的矩阵方法

Matrix Method for Arbitrary Order Recursive Relation of General Term

考虑求任意阶递推关系通项的矩阵方法.首先将任意阶递推关系用矩阵表示,求其矩阵的特征值和特征向量,然后把矩阵对角化,最后利用矩阵乘法求得任意阶递推关系的通项.

The paper introduces matrix to obtain arbitrary order recursive relation. First of all,the arbitrary order recursive relation is transformed into matrix in an effort to determine the eigenvalue and eigenvector of the matrix,and then the matrix is transformed into diagonalization marix. Finally,arbitrary order recursive relations of general term is obtained using the matrix multiplication.