文[1],[2]介绍了将递推关系改写成矩阵形式,从而求数列通项的问题转化为求矩阵方幂的问题,然后利用矩阵对角化思想求矩阵方幂.此时容易联想到特征理论,而哈密尔顿-凯莱定理是矩阵特征多项式的一个重要性质.本文拟用哈密尔顿-凯莱定理求双线性递推数列通项.由[3]知矩阵A与对角矩阵相似充要条件是A的初等因子全为一次的.当A的不变因子有重根时,矩阵A不与对角矩阵相似.本文介绍可对角化和不可对角化双线性递推数列通项的求 In [1], [2], the recursion relation is rewritten into a matrix form so that the problem of solving the general term in the sequence is transformed into the problem of solving the power of the matrix. Then, the matrix diagonalization of the matrix is ​​used to find the matrix power. The Hamiltonian-Caleb’s theorem is an important property of the matrix characteristic polynomial.This paper intends to use the Hamilton-Caleb theorem to find the bilinear recursive sequence generalization [3]. The matrix A is similar to the diagonal matrix The necessary and sufficient condition is that the elementary factors of A are all once, and the matrix A is not similar to the diagonal matrix when the invariant factors of A have heavy roots.This paper introduces the bilinear recursion sequence diagonalization and non-diagonalization Requirements of the item