关于Cramer法则的再推广与应用  

On the Re-generalization and Application of Cramer’s Rule

作　　者：郑振 邓勇 ZHENG Zhen;DENG Yong(College of Mathematics and Statistics,Kashi University,Kashi 844000,Xinjiang,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000

出　　处：《喀什大学学报》2020年第3期12-15,共4页Journal of Kashi University

摘　　要：众所周知,任何相容线性方程组等价于系数矩阵A行满秩的线性方程组Ax=b,并且其最小范数解A+由Moore-Penrose求逆公式A+=A(*AA*)-1给出,其中x∈Rm,b∈Rn,A=(aji)是一个n×m(m≥n)阶实矩阵.为便于解x=A+b的程序化计算,利用Cramer法则和Burgstahler定理得到了其用行列式表示的两个新公式.特别地,当m=n时,这两个公式与著名的Cramer公式完全一致.It is well-known,the necessary and sufficient condition for consistent linear system of equations Ax=b has solutions is full rank of the coefficient matrix A,and its minimum norm solution A+is given by the Moore-Penrose inversion formula A+=A*(AA*)-1,where x∈Rm,b∈Rn,A=(aji)is an n×m(m≥n)real matrix.In order to the programmatic calculation of x=A+b easily,two new formulas which express in a determinant are obtained by Cramer’s rule and Burgstahler’s theorem.In particular,when m=n,these two formulas are same as the famous Cramer’s formula exactly.

关 键 词：CRAMER法则 Burgstahler定理 广义Cramer公式 线性方程组 

分 类 号：O241.6[理学—计算数学]