| 幂幺矩阵的充要条件 |
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| 引用本文： | 唐建国,严青云.幂幺矩阵的充要条件[J].数学的实践与认识,2010,40(20). |
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| 作者姓名： | 唐建国 严青云 |
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| 摘 要： | 研究幂幺矩阵的充要条件,利用矩阵的秩和齐次线性方程组解空间的维数.将m=2时幂幺矩阵的充要条件推广到一般幂幺矩阵的充要条件,得出了幂幺矩阵可对角化的结果,并将幂幺矩阵的充要条件平行地推广到幂幺线性变换.
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| 关 键 词： | 幂幺矩阵 充要条件 矩阵的秩 解空间的维数 |
Necessary and Sufficient Conditions for Unit-Ponent Matrices |
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| TANG Jian-guo,YAN Qing-yun.Necessary and Sufficient Conditions for Unit-Ponent Matrices[J].Mathematics in Practice and Theory,2010,40(20). |
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| Authors: | TANG Jian-guo YAN Qing-yun |
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| Abstract: | Necessary and sufficient(NS) conditions for unit-ponent matrices are explored. A NS condition for unit-ponent matrices as m=2 is generalied to general unit-ponent matrices by using rank of matrices and dimension of solution spaces of homogeneous linear systems,and a result that unit-ponent matrices are diagonalizable is obtained.Finally, the NS conditions for unit-ponent matrices are parallelly generalied to unit-ponent linear transformations. |
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| Keywords: | unit-potent matrix necessary and sufficient condition rank of matrix dimension of solution space |
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