实对称矩阵对角化的研究

Research on Diagonalization of Real Symmetric Matrix

若实对称矩阵可对角化,则存在正交矩阵,使其相似于对角矩阵,且正交矩阵的选取不是唯一的。探讨了实对称矩阵正交对角化过程中选取的正交矩阵之间的关系,并举例说明。

If a real symmetric matrix was diagonalizable, then there existed an orthogonal matrix which can make the real symmetric matrix similar to a diagonalization matrix, and the real symmetric matrix was not u-nique.We discussed the relationship between the orthogonal matrices in the process of orthogonal diagonalization of real symmetric matrix, and an example was given to explain it.