实对称矩阵转化为对角矩阵方法及应用

Methods and Application of Transforming Real Symmetric Matrix into Diagonal Matrix

研究了非负矩阵的对角化问题,证明可逆变换矩阵经正交化得到正交矩阵后,进而实现实对称矩阵的相似对角化。非负实对称矩阵在何种条件下实现对角化,这一问题值得深入探讨,从矩阵的方法入手,涉及其在各个方面的应用,从多个角度进行分析,对该类矩阵进行详细说明及解释。

In this paper,the diagonalization of non-negative matrix is studied,and it is proved that the orthogonalization of invertible transformation matrix produces orthogonal matrix,and then the similar diagonalization of real symmetric matrix is realized.Under what conditions the non-negative real symmetric matrix can be diagonalized,this problem is worth in-depth discussion.This paper starts with the method of matrix,involves its application in various aspects,analyzes it from multiple angles,and explains this kind of matrix in detail.