几个n维Euclid空间概念与定理  

Several Important Concepts and Theorems for the n Dimension Euclid Space

作　　者：刘道建[1] 

机构地区：[1]湖南科技大学数学与计算科学学院 湖南湘潭411201

出　　处：《湖南工程学院学报（自然科学版）》2006年第3期80-82,共3页Journal of Hunan Institute of Engineering(Natural Science Edition)

基　　金：湖南科技大学科研项目"线性规划问题的几何算法"

摘　　要：解析几何中介绍了三维Euclid空间中点、直线、平面的概念及关系,通过把三维Euclid空间中向量的数性积、矢性积与混合积等推广到n维Euclid空间的情形,研究了n维Euclid空间中向量间的关系,以此为基础,推广了点、直线、平面的概念,尤其给出了n维Euclid空间中关于点、直线、平面的几个重要关系定理,为线性规划的几何算法研究打下了理论基础.Analytic geometry is involved in the concepts of point, straight line and plane of the three dimensions space and their relations. In this paper, the n dimension vector relations are studied by generalizing the concepts of vector quantity product, vector product and mixed product from the three space to the n dimension space. Meanwhile, the concepts of point, straight line and plane are generalized to the case of the n dimension space. This paper also gives several important relation theorems between the n dimension point, straight line and plane, which lays a solid theoretical foundation for the linear programming geometry algorithm.

关 键 词：n维Euclid空间 概念 定理 性质 

分 类 号：O151.21[理学—数学]