求解奇异线性方程组的一类推广的Cramer法则  

A Category of Extended Cramer Rule for Solutions of Singular Equations

作　　者：蔡静[1] 

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2006年第1期19-24,共6页Journal of Huzhou University

基　　金：2004年度校级科研立项项目(200322);教育厅科研项目(20030594);湖州师范学院科研基金项目(200302)

摘　　要：任意给定方阵A,首先给出了A的群逆、Dazin逆的行列式表示,借此导出了求一类约束线性方程组的解的行列式公式,并应用文献[8]的结果,得到了求不相容线性方程组极小范数最小二乘解的行列式公式.当方程组为非奇异线性方程组时,所得行列式公式均可化为经典的Cramer法则,从而将Cramer法则在奇异线性方程组领域做了新的形式的推广.In this paper, for any given square matrix A＇, the author presents a determinantal representa- tion for the group inverse and theDrazin inverse of A, from which he obtains the determinantal formulas for solutions of a restricted linear equations and he also gets a determinantal formula for the minimum - norm least - squares solution of inconsistent linear equations. All the determinantal formulas given in this paper are reduced to the common Cramer rule in the case of nonsingular linear equations. Hence the results of this paper are new extensions of Cramer rule for singular linear equations.

关 键 词：群逆 Dazin逆 最大非奇异子阵 M-P逆 CRAMER法则 

分 类 号：O151.21[理学—数学]