正交投影算子乘积广义逆的表示及其性质  

The Representations of the Generalized Inverses of the Products of Orthogonal Projection Operators and Its Properties

作　　者：靳宏伟[1] 

机构地区：[1]湖南大学数学与计量经济学院,长沙湖南410082

出　　处：《数学进展》2015年第6期809-815,共7页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11571098)

摘　　要：本文利用正交投影算子分块形式的表示式,给出了两个投影算子P,Q乘积的MoorePenrose逆以及Drazin逆的表示,并利用所得结果给出了P,Q乘积Drazin逆的相关等式和性质.最后得到了投影算子P,Q的Moore-Penrose逆以及Drazin逆反序律之间的等价关系.In this paper, the representations for the Moore-Penrose inverse and Drazin inverse of the products of orthogonal projection operators P, Q are given by using the expression of the block form of them. Based on the results obtained, the related equalities and properties of the Drazin inverse of the products of P, Q are also given. Finally, we give the equivalent conditions concerning the reverse order law of the Moore-Penrose inverse and Drazin inverse of the orthogonal projectors P, Q.

关 键 词：正交投影算子 MOORE-PENROSE逆 DRAZIN逆 反序律 

分 类 号：O151[理学—数学] O177.1[理学—基础数学]