摘要
来自工程和科学研究领域的许多问题,最终都需要求解几何约束问题.距离几何中的各种度量方程为解决涉及几何度量的几何约束问题提供了数学基础,同时是研究正定和非正定距离几何的基础内容和基本工具.通过提出广义抽象距离空间的概念,消除抽象距离空间距离矩阵对称的这一限制条件,建立了广义抽象距离空间的秩的基本定理,作为建立在欧氏空间和非欧空间中的广义抽象距离空间的度量基础,给出了几个具体的有限齐秩广义抽象距离空间的广义度量方程.利用这些广义度量方程,为求解更为复杂的几何约束问题提供了所必需的各种代数方程.
Many problems involving the engineering and science research are the solving geometric constraints problems.Each metric equation of distance geometry provides one of the mathematical foundation and the basic tools to settle the geometric constraints problems referring to the geometry metric.Also,it is one of the fundamental contents and the basic tools for researching positive definite and non-positive definite distance geometry.In this paper,by introducing a concept of a generalized abstract distance space,the basic theorem of the rank of a generalized abstract distance space is established without the assumption that the metric matrix is symmetry in the generalized abstract distance space.As metric basics of a generalized abstract distance space establishing in Euclidean space and non-Euclidean space,several specific generalized metric equations of generalized abstract distance space are achieved.By using these generalized metric equations,some algebraic equations for solving many more complex geometric constraint problems are given.
出处
《浙江大学学报（理学版）》
CAS
CSCD
北大核心
2010年第3期263-268,共6页
Journal of Zhejiang University（Science Edition）
基金
国家自然科学基金资助项目(10901116)
关键词
几何约束
距离几何
抽象距离空间
秩
判别式
广义度量方程
geometric constraints
distance geometry
generalized abstract distance space
rank
discrimination formula
generalized matric equation
