关于线性方程组A_(mn)X_(n1)=B_(m1)相关问题的探讨  

Study on the problem of linear equations A_(mn)X_(n1)=B_(m1)

作　　者：栾林[1] 

机构地区：[1]辽宁省交通高等专科学校现代教育技术中心,辽宁沈阳110122

出　　处：《辽宁师范大学学报（自然科学版）》2010年第2期165-167,共3页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：在求解线性方程组时通常采用矩阵的初等变换的方法,或当系数矩阵可逆时利用逆矩阵进行求解.讨论一种新的线性方程组的矩阵解法,即利用矩阵广义逆的理论求解线性方程组.分析满秩矩阵、弱逆矩阵定义,利用一个矩阵是另一个矩阵的弱逆阵的充要条件得出任意m×n矩阵必有弱逆阵且不唯一的结论,给出弱逆阵的求法,进而给出了线性方程组一种新的矩阵解法.The method of elementary transformation is often used in solving linear equations.If the matrix of coefficient is an invertible matrix,the inverse of matrix to solve the linear equations is used.This paper demonstrates a new method of solving linear equations—using the theory of the generalized matrix to solve linear equations.Firstly,it presents the definitions of the full rank matrix and weak inverse of matrix,and then it comes to conclusion that any one m×n matrix must have an non-unique weak inverse of matrix by means of using the necessary and sufficient condition that a matrix is the weak inverse of another matrix,finally,it gives the solving method of a weak inverse of matrix and a new method of solving linear equations by the matrix.

关 键 词：线性方程组 秩 满秩矩阵 弱逆矩阵 初等变换 

分 类 号：O151.21[理学—数学]