Introduction to Geometric Algebra, a powerful tool for mathematics and physics

Abstract

In this thesis an introduction to geometric or Clifford algebra is given, with an emphasis on the geometric aspects of this algebra. The aim is to show that this algebra is a powerful tool for both mathematics and physics and results in compact, coordinate free expressions. The main focus will be on Euclidean spaces of 2 and 3 dimensions, but it will be shown that it is possible to extend the results to higher dimensions. Finally a start will be made to further extend to more general algebras with non-degenerate bilinear forms with a mixed signature.