矩阵及其多项式的对角化

On the Diagonalization of a Matrix and Its Polynomial

设矩阵B是矩阵A的多项式,那么矩阵A的特征向量一定是矩阵B的特征向量.当矩阵A可相似于对角矩阵时,矩阵B也一定可以相似于对角矩阵.但反之未必成立.当矩阵B可相似于对角矩阵时,文中给出了矩阵A必定相似于对角矩阵的充分条件.

Let B be a polynomial of the matrix A, then eigenvectors of A must be eigenvectors of B. When A is diagonal- izable then B is for sure diagonalizable. But the conversa may not be necessarily true. Sufficient conditions for A being surely diagonalizable are given when B is diagonalizable.