实对称矩阵与规范正交基的本质关系研究

Real Symmetrical Matrix and Orthogonal Basis

研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基.利用特征值、特征向量、正交化等概念,通过欧氏空间中的对称变换、度量矩阵、正交矩阵,证明了实对称矩阵、对角矩阵以及欧氏空间的规范正交基之间内在的,虽非唯一性、而却是本质性的对应关系.

The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied. By researching the symmetric transformation,measure matrix and orthogonal matrix, we obtain the relation system among the real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space. It is inherent and natural.