从关系空间到欧氏空间

从实二阶矩空间L2出发,以协方差作为内积,使L2成为关系空间,在建立了常元、范数、距离、依范数收敛等概念基础上,论述了L2是一个完备的内积空间;在L2中又定义了夹角、正交、坐标、正交系等概念,以不共线为标准张成的子空间与欧氏空间相关联,使L2中的问题处理转化为普通向量的问题处理。

From Relation Space to Euclidean Space

In this paper the real space L_2 with second order moment is considered. We present that L_2 is a relation with covariance as its inner product. After constructing concepts of constant element, norms, distance and convergence in norm, we point out that L_2 is also a complete inner product space. Finally we define angle, orthogonality, coordinates and orthogonal system and prove that spanning sub-space based on the standard of non collinear is incident to Euclidean space. Thus the problem in L_2 can be convert to that of Euclidean space.