The Null and Column Spaces of Combinations of Two Projectors
Received:June 04, 2015  Revised:September 14, 2015
Key Words: projector   orthogonal projector   null space   column space  
Fund Project:Supported by the Tianyuan of National Natural Science Foundation of China (Grant No.70871050) and the Youth Project of Education Department of Hubei Province (Grant No.B20122203).
Author NameAffiliation
Tao XIE Faculty of Mathematics and Statistics, Hubei University, Hubei 430062, P. R. China
Faculty of Mathematics and Statistics, Hubei Normal University, Hubei 435002, P. R. China 
Xiaokun ZHU School of Mathematic and Statistic, Central China Normal University, Hubei 430079, P. R. China 
Kezheng ZUO Faculty of Mathematics and Statistics, Hubei Normal University, Hubei 435002, P. R. China 
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Abstract:
      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 $P\pm Q$ 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 $\mathcal{N}(PQ+QP)$ and $\mathcal{N}(PQ-QP)$ is discussed and necessary and sufficient conditions for them to be equal are also studied.
Citation:
DOI:10.3770/j.issn:2095-2651.2016.04.003
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