## 矩阵广义逆的某些性质与应用

The Property of Generalized Inverse and Its Application
Abstract: Generalized inverse of a matrix is a generalization of the inverse of a singular matrix. Generalized inverses of matrices play an important role in many questions. Especially, it can be used to sole linear equations, and it provides a shortcut to solve complex linear equations. The present paper introduces the concept of generalized inverse, investigates the properties of generalized inverse and the method to obtain to generalized inverse, discusses some types of generalized inverse which is used to solve linear equations, and studies the Moore-Penrose inverse by angles from one subspace to another and angles between two subspaces.
Keywords:    generalized inverse; Moore-Penrose inverse; linear equations; angles between two subspaces; reduced minimum modulus

Abstract    i

1    绪论    1
1.1    课题的目的和意义    1
1.2    国内外研究现状与发展趋势    1 源自六/维-论;文;网!加7位QQ324,9114 www.lwfree.cn
2    矩阵广义逆的概念与性质    3
2.1    矩阵广义逆的基本概念    3
2.2    减号逆    3
2.3    自反广义逆    4
2.4    最小范数广义逆    5
2.5    最小二乘广义逆    6
2.6    加号逆    6
3    矩阵广义逆的计算方法    8
3.1    满秩长方阵的广义逆的概念    8
3.2    矩阵广义逆的计算方法    8
3.2.1    初等变换法    8
3.2.2    满秩分解法    9
4    广义逆在解线性方程组中的应用    12
4.1    线性方程组的求解问题    12
4.2    相容方程组的通解与减号逆    13
4.3    相容方程组的极小范数解与最小范数广义逆    14
4.4    不相容方程组的最小二乘解与最小二乘广义逆    15
4.5    加号逆在线性方程组的求解中的应用    17
5    子空间夹角与Moore-Penrose逆    21
6    结论    24

1    绪论
1.1    课题的目的和意义

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