关于两个投影矩阵的相互关系  

Relationship between two projection matrices

作　　者：周玉兴[1] 黄宗文[2] 

机构地区：[1]广西师范学院师园学院,广西南宁530226 [2]广西大学行健文理学院,广西南宁530005

出　　处：《西南民族大学学报（自然科学版）》2015年第2期221-223,共3页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(11161004);广西自然科学基金(2013GXNSFAA019008)

摘　　要：运用Moore-Penrose逆的定义及其性质和投影的定义去研究投影PR(A)和PR(AB)的相互关系,得到若干结果 .研究表明:若矩阵A,B满足如下条件:(1)BB*=I,(2)B为酉矩阵,(3)B为非奇异阵,(4)A是列满秩,B是行满秩,则两者相等;若对于任意矩阵A,B时,两者之间存在若干重要关系式,从而进一步刻画了它们的相互关系.This paper uses the definition and properties of Moore＊Penrose inverse and the definition of projection to study the relationship bdtween the projection PR（A） and P（AB） ,and some results are obtained. Research shows that if the matrices A and B satisfy the following conditions ： （ 1 ）. BB ^＊ = I; （2）. B is a unitary matrix; （ 3 ）. B is a non-singular matrix; （4）. A is full column rank and B is a full row rank, then they are equal. For any matrices A and B, there are several important relationships between the two. Thus the paper further describes the relationship between them.

关 键 词：MOORE-PENROSE逆 投影 矩阵 

分 类 号：O151.21[理学—数学]