| m次幂等矩阵的等价条件 |
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| 引用本文： | 陈益智.m次幂等矩阵的等价条件[J].数学的实践与认识,2011,41(23). |
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| 作者姓名： | 陈益智 |
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| 作者单位： | 广东惠州学院数学系,广东惠州 516007;西北大学数学系,陕西西安 710127 |
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| 基金项目： | 广东省自然科学基金(8151601501000002,9151051501000066); 广东惠州学院项目(C_210·0216,C_211·0106,JG2010008) |
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| 摘 要： | 利用矩阵的秩和齐次线性方程组解空间的维数,给出了m(m≥2)次幂等矩阵的一些等价条件,推广了2,3次幂等矩阵的相应结果.此外,所获结果还给推广到了m次幂等线性变换中.
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| 关 键 词： | m次幂等矩阵 矩阵的秩 齐次线性方程组 解空间的维数 m次幂等线性变换 |
Equivalent Conditions for m Times Idempotent Matrices |
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| CHEN Yi-zhi.Equivalent Conditions for m Times Idempotent Matrices[J].Mathematics in Practice and Theory,2011,41(23). |
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| Authors: | CHEN Yi-zhi |
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| Institution: | CHEN Yi-zhi (Department of Mathematics,Huizhou University,Huizhou 516007,China) (Department of Mathematics,Northwest University,Xi'an 710127,China) |
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| Abstract: | In this paper,some equivalent conditions for m(m≥2) times idempotent matrices are given by using rank of matrices and dimensions of solution spaces of homogeneous linear systems.Consequently,the results as m=2 and m=3 are generalized.Also,the corresponding results are generalized to m times idempotent linear transformations. |
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| Keywords: | m times idempotent matrices rank of matrices homogeneous linear systems dimensions of solution spaces m times idempotent linear transformations |
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