广义逆矩阵与相容线性方程组

 广义逆矩阵与相容线性方程组

摘要: 本系统地论述与相容线性方程组相关2种广义逆矩阵的定义、性质和计算，以及与相容线性方程组的关系．前言从引进广义逆矩阵的定义着手，介绍了它的历史概况以及发展的背景及其意义；第1章从广义逆的发展历程讨论由Moore-Penrose方程确定的各种广义逆的定义；第2章讨论广义逆中的减号逆A 的定义及性质以及在相容线性方程组的应用；第3章讨论广义逆中的最小范数逆A 的定义及计算以及它与相容线性方程组Ax=b的极小范数解．全文全面地给出与相容线性方程有关的2种广义逆矩阵的定义、性质、计算及其在相容线性方程组中的应用．
关键词: 广义逆矩阵；极小范数解；线性方程组

Generalized Inverse Matrix and
Compatible Linear Equations

Abstract:  This paper systematically discussed the definition, nature and calculation of two kinds of generalized inverse matrix related to the compatible linear equations, and their relations with the compatible linear equations. The preface gave the definition and introduced history, background of development and significance of generalized inverse matrix. The first chapter, from the development process of generalized inverse, discussed all kinds of definition of generalized inverse determined by the Moore - Penrose equations. The second chapter discussed the definition and nature of dashes inverse A in generalized inverse as well as its application in compatible linear equations. The third chapter discussed the definition and calculation of the minimum norm inverse A  in generalized inverse, as well as the Minimal Norm Solution of its compatible linear equations Ax = b. The whole text completely provided the definition, nature and computation of two kinds of generalized inverse matrix related to the compatible linear equation and its application in the compatible linear equations.