投影矩阵序的判定定理的一种证明

A Kind of Proof for Decision Theorem of the Projection Matrix Order

利用初等矩阵理论的方法,证明了投影矩阵序的判定定理,此定理是研究复杂系统的第二条基础定理.对称分析理论和正交分析理论是研究复杂系统的基本理论,矩阵象是研究对称性和正交性的主要工具,此定理的主要作用是研究处理矩阵象的序运算规律,这些规律是提出的GL算法、零成分搜索法、对称性全局方差分析、正交性全局方差分析等起源于东方文化的新方法的数学基础.

Using the theory of elementary matrix, this paper proves the decision theorem of the projection matrix order which is the second fundamental theorem to study the complicated system. As symmetric analysis theory and orthogonal analysis theory are the two fundamental theories to study complicated system, and matrix image is the main tool to study symmetry and orthogonality, the decision theorem is mainly used to study the op- eration law of matrix image which is the base of the new eastern culture - oriented methods, such as GL, zero el- ement search method, symmetry global variance analysis and orthogonality global variance analysis and so on.