矩阵的特征根与特征向量及其相似对角形的优化求法

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

研究了矩阵的特征根与特征向量及其相似对角形的优化求法.优化了文[1]的方法,只要对矩阵A的特征矩阵λE-A施行初等变换化为对角形,即可同时求出A的特征根与特征向量,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^(-1)AT为对角形矩阵.

In this paper, a optimized method for the characteristic values, the characteristic vectors and the resemble diagonal form of a matrix is studied. With the optimized 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 more easily.