| 每个矩阵都能表成两个秩幂等矩阵之和 |
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| 引用本文： | 左可正.每个矩阵都能表成两个秩幂等矩阵之和[J].湖北师范学院学报(自然科学版),2008,28(4). |
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| 作者姓名： | 左可正 |
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| 作者单位： | 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： | 湖北师范学院资助项目
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| 摘 要： | 研究了秩幂等矩阵的性质及两个秩幂等矩阵的线性组合的结构,利用矩阵的广义逆,矩阵的若当标准形与矩阵的有理标准形,得出了秩幂等矩阵的一些新的特征,并证明了每个矩阵都能表成两个秩幂等矩阵之和。
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| 关 键 词： | 秩幂等矩阵 若当标准形 Moore-Penrose逆 群逆 |
Everymatrix is a sum of two rank-idempotent matrices |
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| ZUO Ke-zheng.Everymatrix is a sum of two rank-idempotent matrices[J].Journal of Hubei Normal University(Natural Science),2008,28(4). |
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| Authors: | ZUO Ke-zheng |
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| Institution: | ZUO Ke-zheng(College of Mathematics and Statistics; Hubei Normal University; Huangshi 435002; China); |
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| Abstract: | This paper researches some properties of rank-idempotent matrix,and the linear combinations structures of two rank-idempotent matrices.By using the generalized inverse of matrix,the Jordan canonical form of matrix and the rational canonical form of matrix,we get some new characters of rank-idempotent matrix,and prove that every matrix is a sum of two rank-idempotent matrices. |
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| Keywords: | rank-idempotent matrix Jordan s canonical form Moore-Penrose inverse group inverse |
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