| 幂等矩阵与秩幂等矩阵的充要条件 |
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| 引用本文： | 刘小川,何美.幂等矩阵与秩幂等矩阵的充要条件[J].雁北师范学院学报,2011,27(1). |
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| 作者姓名： | 刘小川 何美 |
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| 作者单位： | 山西大同大学数学与计算机科学学院,山西大同,037009 |
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| 摘 要： | 满足A2=A的n阶方阵A称为幂等矩阵,它是矩阵环Mn（F）的一个幂等元;满足r（A）=r（A2）的n阶方阵A称为秩幂等矩阵。它们与空间的分解、不变子空间的研究有密切关系。利用线性空间的理论方法研究幂等矩阵与秩幂等矩阵的性质,分别得到与它们等价的一些充要条件。
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| 关 键 词： | 幂等矩阵 秩幂等矩阵 矩阵的核 矩阵的列空间 矩阵的秩 |
The Necessary and Sufficient Conditions for Idempotent Matrix and Rank-idempotent Matrix |
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| LIU Xiao-chuan,HE Mei.The Necessary and Sufficient Conditions for Idempotent Matrix and Rank-idempotent Matrix[J].Journal of Yanbei Teachers College,2011,27(1). |
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| Authors: | LIU Xiao-chuan HE Mei |
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| Institution: | LIU Xiao-chuan,HE Mei(School of Mathematics and Computer Science,Shanxi Datong University,Datong Shanxi,037009) |
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| Abstract: | A matrix of satisfying A= A2 is called idempotent matrix.It is an idempotent element of matrix ring Mn（F）.A matrix of satisfying r（A）= r（A2） is called rank-idempotent matrix.They are closely related to decomposition of space and invariant subspace.Some properties of idempotent matrix and rank-idempotent matrix are discussed by using methods of linear space.The necessary and sufficient conditions for idempotent matrix and rank-idempotent matrix are given. |
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| Keywords: | idempotent matrix rank-idempotent matrix kernel of matrix column space of matrix rank of matrix |
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