| 两个投射子组合的核空间与列空间 |
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| 引用本文： | 谢涛,朱小琨,左可正.两个投射子组合的核空间与列空间[J].数学研究及应用,2016,36(4):407-422. |
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| 作者姓名： | 谢涛 朱小琨 左可正 |
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| 作者单位： | 湖北大学数学与统计学学院, 湖北 武汉430062; 湖北师范学院数学与统计学院, 湖北 黄石 435002,华中师范大学数学与统计学院, 湖北 武汉 430079,湖北师范学院数学与统计学院, 湖北 黄石 435002 |
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| 基金项目： | 国家自然科学基金天元基金(Grant No.70871050), 湖北省教育厅青年项目(Grant No.B20122203). |
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| 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 N(P Q + QP) and N(P Q- QP) is discussed and necessary and sufficient conditions for them to be equal are also studied.
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| 关 键 词： | projector orthogonal projector null space column space |
| 收稿时间： | 6/4/2015 12:00:00 AM |
| 修稿时间： | 2015/9/14 0:00:00 |
The Null and Column Spaces of Combinations of Two Projectors |
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| Tao XIE,Xiaokun ZHU and Kezheng ZUO.The Null and Column Spaces of Combinations of Two Projectors[J].Journal of Mathematical Research with Applications,2016,36(4):407-422. |
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| Authors: | Tao XIE Xiaokun ZHU and Kezheng ZUO |
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| Institution: | 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,School of Mathematic and Statistic, Central China Normal University, Hubei 430079, P. R. China and 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. |
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| Keywords: | projector orthogonal projector null space column space |
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