R^n上的投影阵与不相容线性方程组的最优解  

Projection Matrix on R^n and the Optimal Solution of Inconsistent Linear Simultaneous Equations

作　　者：郭华[1] 

机构地区：[1]渝州大学数学与计算机科学系,重庆400033

出　　处：《渝州大学学报（自然科学版）》2002年第1期14-17,共4页Journal of Yuzhou University(Natural Sciences Edition)

摘　　要：研究了所有n维实向量构成的线性空间Rn上的投影阵 ,从线性变换的角度给出了投影阵定义 ,讨论了其性质 ,指出了Rn上一般投影阵与P=A(ATA) 1 AT 之间的关系 ,以及与不相容性方程组的最优解之间的紧密联系。The projection matrixes on linear space R n composed of all n_dimension real vectors was studied. The definition of projection matrix was given with the view of linear transform,and its properties were also discussed. Furthermore,the realtions between general projection matrix and P=A TA) -1 A T on R n ,and between that and the optimal solution of inconsistent linear simultaneous equations were pointed out.

关 键 词：最优解 线性空间R^n 投影阵 投影变换 投影向量 实幂等矩阵 列空间 核空间 不相容线性方程组 

分 类 号：O151.21[理学—数学]