广义度量方程的改进及其应用(Ⅰ)  

THE IMPROVEMENT OF GENERALIZED METRIC EQUATIONS AND APPLICATIONS(Ⅰ)

作　　者：杨定华[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066

出　　处：《系统科学与数学》2009年第3期425-432,共8页Journal of Systems Science and Mathematical Sciences

基　　金：四川省教育厅重点自然科学基金(07ZA087)资助课题.

摘　　要：众所周知,度量方程作为距离几何的基本内容和工具之一,在几何约束求解中扮演着主要的角色.改进了杨定华关于n维欧氏空间中两个等数量有限基本元素构成集合的广义度量方程,建立了更为一般意义的、应用方便的广义度量方程,作为其初步应用,导出了两个单形之间的一些有趣的矩阵恒等式关系.特别地,将其两边取行列式,可以简洁得到关于联系两个单形的几何恒等式.It is well known that metric equations are one of the basic contents and tools in distance geometry, and play a center role in solving the problems of geometric constraints. In this paper, the generalized metric equations involving two finite sets of elementary material in higher dimensional Euclidean space given by Yang D H is improved, it is more convenient to research the relations of two simplexes by using the new generalized metric equations. As its applications, some fimny geometric relations involving two simplexes are given, especially, the geometric identity involving two simplexes given by Yin J Y and Chen F J is infered.

关 键 词：高维欧氏空间 单形 体积 基本元素 广义度量方程 矩阵恒等式 

分 类 号：O184[理学—数学]