The Null and Column Spaces of Combinations of Two Projectors  

作　　者：Tao XIE Xiaokun ZHU Kezheng ZUO 

机构地区：[1]Faculty of Mathematics and Statistics,Hubei University,Hubei 430062,P.R.China [2]School of Mathematic and Statistic,Central China Normal University,Hubei 430079,P.R.China [3]Faculty of Mathematics and Statistics,Hubei Normal University,Hubei 435002,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2016年第4期407-422,共16页数学研究及应用（英文版）

基　　金：Supported by the Tianyuan of National Natural Science Foundation of China(Grant No.70871050);the Youth Project of Education Department of Hubei Province(Grant No.B20122203)

摘　　要：This paper establishes some new equalities and inequalities for the null and column spaces of combinations of two projectors P and Q. Some new necessary and sufficient conditions for P ± Q to be invertible are given by the structure of null and column space of some combinations of P and Q. In addition, the inclusion relation of Af（PQ ＋ QP） and N（PQ - QP） is discussed and necessary and sufficient conditions for them to be equal are also studied.This paper establishes some new equalities and inequalities for the null and column spaces of combinations of two projectors P and Q. Some new necessary and sufficient conditions for P ± Q to be invertible are given by the structure of null and column space of some combinations of P and Q. In addition, the inclusion relation of Af（PQ ＋ QP） and N（PQ - QP） is discussed and necessary and sufficient conditions for them to be equal are also studied.

关 键 词：PROJECTOR orthogonal projector null space column space 

分 类 号：O177[理学—数学]