Other Physical Sciences and Mathematics Commons^™

Arrow Spaces: A Unified Algebraic Approach To Euclidean Geometry And Inner Product Spaces, Hussin M. Albahboh

Graduate Theses, Dissertations, and Problem Reports

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 an inner product vector space over R. Using this arrow space pre-inner product, various properties of the arrow space are derived and contrasted with the properties of a vector space over R. The axioms …