矩阵的特征根与特征向量及其相似对角形的统一求法

On the Uniform Method for the Characteristic Values,the Characteristic Vectors and the Resemble Diagonal Matrix of a Matrix

给出了解决矩阵对角化问题的一个简便方法.应用这个方法,可同时求出A的特征根及特征向量,判断A是否可对角化,在A可对角化时,可直接写出相应的可逆矩阵T,使T-1AT为对角形矩阵.

In this paper, a simple and convenient method for the diagonalization of a matrix is given. With the method, we can obtain the characteristic values and the characteristic vectors, judge the diagonalization of the matrix, write out the reversible matrix T satisfying T^1-AT is a diagonal matrix if A is a diagonalization matrix at the same time.