Türk Uzaktan Algılama ve CBS Dergisi

Öz

In this paper algebraic construction of a novel geometry, which unifies inner and outer product spaces, as well as inner and outer product operations have been explained. This novel approach is called geometric algebra and also referred as Clifford algebra in the literature. It is expected that geometric algebra will bring novelties to engineering fields with its more effective rotation properties than quaternions and easier structures than tensor algebra. For easy understanding of the structures of the geometric algebra, its first constructive axioms and their use for constructing the algebra, should be clearly understood. In this paper, those constructive axioms are defined and explained how to use them to construct the geometric algebra. Once the algebra is constructed, it is straight to generalize it to upper dimensional spaces. With geometric algebra, it is easier to explain geometric relationships in the upper dimensions than classical algebras, also in situations that the classical approaches are insufficient. For example, the projective geometry can deeply be analyzed by compact structure of the geometric algebra in 4-dimensional algebraic space. In 5-dimensional geometric algebraic space, analysis of the conformal geometry is very effective. The paper aims at introducing geometric algebra with its constructive first axioms and explain the construction of the geometry in a tractable manner.