论文标题
箭头空间：内部产品空间和仿射几何形状的方法
Arrow Spaces: An Approach to Inner Product Spaces and Affine Geometry
论文作者
论文摘要
给定一组要点，为“箭头空间”提出了公理的代数系统。箭头被定义为分别命名为尾部和头部的两个点<t，h>的有序集。箭头集是箭头空间。箭头空间被公理地赋予箭头空间“预先产物”，该产品类似于欧几里得矢量空间的内部产物。使用此箭头空间预入产品，得出了箭头空间的各种特性，并与欧几里得矢量空间的属性进行了对比。矢量空间的公理及其相关的内部产物是从箭头空间的公理遵循的定理中得出的，因为严格证明向量是箭头的等效类别。提供了使用箭头空间解决仿射几何形状中的几何问题的应用。
Given a postulated set of points, an algebraic system of axioms is proposed for an "arrow space'". An arrow is defined to be an ordered set of two points <T, H>, named respectively Tail and Head. The set of arrows is an arrow space. The arrow space is axiomatically endowed with an arrow space "pre-inner product" which is analogous to the inner product of a Euclidean vector space. Using this arrow space pre-inner product, various properties of the arrow space are derived and contrasted with the properties of a Euclidean vector space. The axioms of a vector space and its associated inner product are derived as theorems that follow from the axioms of an arrow space since vectors are rigorously shown to be equivalence classes of arrows. Applications of using an arrow space to solve geometric problems in affine geometry are provided.
