| 数量对合矩阵的线性组合的秩的不变性 |
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| 引用本文： | 张金辉,王海明,杨忠鹏,胡清孝.数量对合矩阵的线性组合的秩的不变性[J].数学研究,2010,43(1):98-103. |
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| 作者姓名： | 张金辉 王海明 杨忠鹏 胡清孝 |
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| 作者单位： | 1. 莆田学院数学系,福建,莆田,351100
2. 莆田学院数学系,福建,莆田,351100;福建师范大学数计学院,福建,福州,350007 |
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| 基金项目： | 2008年福建省高校服务海西建设重点项目，福建省教育厅科研资助项目，莆田学院科研资助项目 |
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| 摘 要： | 若矩阵A、B满足A2=λ2I、B2=μ2I（λμ≠0），称A、B都是数量对合矩阵．当非零复数a、b、u、v满足μλ＋bμ≠0、uλ＋vμ≠0时，我们证明了数量对合矩阵A、B与单位矩阵，的线性组合的秩总是相等，并且是一个与a、b、札、u选择都无关的常数．应用所得到数量对合矩阵的线性组合的秩的不变性，可推广已有文献的关于对合矩阵的相应结果．
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| 关 键 词： | 数量对合矩阵 线性组合 秩等式 秩不变性 |
Invariance of Rank for Linear Combinations of Scalar-involutory Matrices |
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| Zhang Jinhui,Wang Haiming,Yang Zhongpeng,Hu Qingxiao.Invariance of Rank for Linear Combinations of Scalar-involutory Matrices[J].Journal of Mathematical Study,2010,43(1):98-103. |
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| Authors: | Zhang Jinhui Wang Haiming Yang Zhongpeng Hu Qingxiao |
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| Institution: | Zhang Jinhui~1 Wang Haiming~1 Yang Zhongpeng~1 Hu Qingxiao~(1,2) (1.Deptment of Mathematics of Putian University,Putian Fujian 351100,2.School of Mathematic , Computer Science,Fujian Normal University,Fuzhou Fujian 350007) |
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| Abstract: | The square matrices A and B over the complex field C are said to be scalar-involutory matrices ff A~2 = λ~2I and B~2 =μ~2I,where λμ≠0.When all nonzero scalars a,b,u,v ∈C satisfying aλ+bμ≠ 0 and uλ + vμ≠0,we proved the rank for the linear combination of a pair of scalar-involutory matrices A,B and a identity matrix I is constant and independent on the choice of a,b,u and v.Then the corresponding results of involutory matrices in previous literatures are generalized by the invariance of rank for linear combinations of scalar-involutory matrices. |
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| Keywords: | scalar-involutory matrices linear combination rank equalities: invariance of rank |
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