| 基于矩阵的二元关系研究 |
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| 引用本文： | 韩俊英.基于矩阵的二元关系研究[J].甘肃农业大学学报,2004,39(4):467-469. |
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| 作者姓名： | 韩俊英 |
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| 作者单位： | 兰州大学信息科学与工程学院,甘肃,兰州,730000;甘肃农业大学信息科学技术学院,甘肃,兰州,730070 |
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| 摘 要： | 对于任意非空有限集合A上的二元关系R,r(R)称为二元关系R的自反闭包,s(R)称为二元关系R的对称闭包,t(R)称为二元关系R的传递闭包。且有ts(R)st(R)。本文旨在提出一个命题,即对于具有自反性质的二元关系R,ts(R)=st(R)。且证明了命题为真。
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| 关 键 词： | 关系矩阵 自反 对称 传递 等价关系 |
| 文章编号： | 1003-4315(2004)04-0467-03 |
Research of the binary relation based on the martrix |
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| HAN Jun-ying.Research of the binary relation based on the martrix[J].Journal of Gansu Agricultural University,2004,39(4):467-469. |
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| Authors: | HAN Jun-ying |
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| Institution: | HAN Jun-ying1,2 |
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| Abstract: | For the the binary relation R based on the nonempty finite set A, r(R) is usually called the relation R抯 reflexive closure , s(R) is its symmetric closure, and t(R) is its transitive closure. And for any general binary relation R,the fact usually is ts(R)st(R). The efforts of this paper are making a proposition, which is for any general reflexive binary relation R, ts(R)=st(R). In addition, the proposition have been proved and verified. |
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| Keywords: | relation matrix reflexive symmetric transitive equivalent relation |
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