| 投影矩阵分解定理的一种证明 |
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| 引用本文： | 罗纯,廖靖宇,张应山.投影矩阵分解定理的一种证明[J].许昌师专学报,2011(5):1-3. |
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| 作者姓名： | 罗纯 廖靖宇 张应山 |
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| 作者单位： | [1]上海应用技术学院理学院,上海200235 [2]许昌学院数学与统计学院,河南许昌461000 [3]华东师范大学金融与统计学院,上海200241 |
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| 基金项目： | 基金项目：教育部高等学校博士学科点专项基金资助项目（44K55050） |
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| 摘 要： | 利用初等矩阵理论方法，证明了投影矩阵分解定理．此定理是研究复杂系统的基础定理．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，而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新方法的数学基础．
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| 关 键 词： | 投影矩阵 正交谱分解 特征向量 矩阵象 |
A Proof for the Projection Matrix Decomposition Theorem |
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| LUO Chun,LIAO Jing-yu,ZHANG Ying-shan.A Proof for the Projection Matrix Decomposition Theorem[J].Journal of Xuchang Teachers College(Social Science Edition),2011(5):1-3. |
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| Authors: | LUO Chun LIAO Jing-yu ZHANG Ying-shan |
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| Institution: | 1. College of Sciences, Shanghai Institute of Technology, Shanghai 200235, China ; 2. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China ; 3. School of Finance and Statistics, East China Normal University, Shanghai 200241, China) |
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| Abstract: | The projection matrix decomposition theorem which is the basic theorem for the study of the complex system is proved by using the elementary matrix theory. Symmetric analysis theory and orthogonal analysis theory are the fundamental theories for the study of the complex system, and matrix images are the main tools to study symmetry and orthogonality. The projection matrix decomposition theorem is mainly used to study operation laws which are the mathematical basis for the study of GL algorithm, zero composition search method, symmetry global variance analysis, and orthogonality global analysis, etc. |
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| Keywords: | projection matrix orthogonal spectral decomposition eigenvector matrix images |
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