陕西师范大学学报：自然科学版2011，Vol.39Issue(6)：10-13,4.
广义逆在幂等算子表示中的应用
Application of generalized inverse to the representations of idempotent operators
摘要
Abstract
By using operator block techniques,the representations of idempotent operators are discussed.It is proved that the necessary and sufficient condition for the operator A（BA）＋ B on a Hilbert space to be an orthogonal projection is that PB＊B=B＊BP,where PB＊B｜R（P） is an invertible operator on R（P）,and PA｜R（A＊B＊） is an invertible operator on R（A＊B＊）（A＋ denote the Moore-Penrose inverse of A）.It is also proved that an idempotent operator P can be represented as the form A（BA）＋ B if and only if PAA＊=AA＊P＊,and an orthogonal projection P can be represented as the form A（BA）＋ B if and only if PAA＊=AA＊P.关键词
幂等算子/分块算子矩阵/Moore-Penrose逆Key words
idempotent/block-operator matrix/Moore-Penrose inverse分类
数理科学引用本文复制引用
窦艳妮,杜鸿科..广义逆在幂等算子表示中的应用[J].陕西师范大学学报：自然科学版,2011,39(6):10-13,4.基金项目
国家自然科学基金资助项目 （）
中央高校基本科研业务费专项资金项目 （）
