矩阵分解理论及应用

本文主要归纳和总结了代数学中的矩阵分解理论及理论应用。本文把矩阵分解分为等价分解、三角分解、谱分解、奇异值分解和Fitting分解等。在论文中对相关理论进行了证明,并给出了矩阵等价分解的一种新的证明方法。在应用方面,展示了等价分解、LU分解、谱分解、奇异值分解和Fitting分解在理论上的应用。

This thesis is an overview of articles,which are summarized and summed up the decomposition of the matrix algebra in the theory and its theoretical applications.Matrix decomposition can be divided into equivalent decomposition,triangular decomposition,spectral decomposition,singular value decomposition,the Fitting decomposition and so on.In this paper,the relevant theory has been proved.Especially,a new method is proposed,which is used to prove the equivalent decomposition of matrix.In applications,the equivalent decomposition,LU decomposition,spectral decomposition,singular value decomposition and Fitting decomposition are introduced.Also,Matlab mathematical software is used to achieve matrix decomposition.It is show that matrix decomposition is practical and simple.