| 保欧氏度量偏序的变换 |
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| 引用本文： | 邓伦治,吴云顺,游泰杰.保欧氏度量偏序的变换[J].数学的实践与认识,2012,42(15):238-243. |
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| 作者姓名： | 邓伦治 吴云顺 游泰杰 |
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| 作者单位： | 贵州师范大学数学与计算机科学学院,贵州贵阳,550001 |
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| 基金项目： | 贵州省科学技术基金，贵州师范大学联合基金 |
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| 摘 要： | 设L(R~n)表示n维欧氏空间R~n的所有线性变换构成的集合,‖ξ‖表示向量ξ的欧氏长度,由欧氏长度建立起向量间的序关系,令:PO(R~n)={f∈L(R~n)■|ξ,η∈R~(n×1),‖ξ‖≤‖η‖■‖f(ξ)‖≤‖f(η)‖}则PO(R~n)是欧氏空间R~n中保欧氏度量偏序变换构成的集合,讨论了PO(R~n)的结构,证明了保持这种序关系的变换由正交变换和伸缩变换组成.
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| 关 键 词： | 变换 序关系 欧氏长度 矩阵 |
Transformation with Keeping Euclidean Measurement Order |
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| DENG Lun-Zhi
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WU Yun-shun
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YOU Tai-jie.Transformation with Keeping Euclidean Measurement Order[J].Mathematics in Practice and Theory,2012,42(15):238-243. |
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| Authors: | DENG Lun-Zhi WU Yun-shun YOU Tai-jie |
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| Institution: | (Department of Mathematics and Computer Science,GuiZhou Normal University Guizhou,Guiyang 550001, China) |
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| Abstract: | Let L(R~n) be the linear transformation on n-dimensional Euclidean space R~n. Let ||ξ|| be the Euclidean length of vectorξ.According to the Euclid length of the vector,set up the order relation about the vector.Let PO(R~n) = {f∈L(R~n)■|ξ,η∈R~(n×1),||ξ||≤||η||■||f(γ)||≤||f(η||} be the transformation with keeping Euclidean measurement order on Euclidean space R~n.In this paper the structure PO{R~n) is studied.It is shown the transformations with keeping the order relation are made up of the Orthogonal transformation and Stretching transformation. |
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| Keywords: | transformation order relation euclidean length matrix |
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