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
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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 Name | Affiliation | 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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