Thesis (M.S.) University of Alaska Fairbanks, 2014We present an axiomatic development of geometric algebra. One may think of a geometric algebra as allowing one to add and multiply subspaces of a vector space. Properties of the geometric product are proven and derived products called the wedge and contraction product are introduced. Linear algebraic and geometric concepts such as linear independence and orthogonality may be expressed through the above derived products. Some examples with geometric algebra are then given.Chapter 1: Preliminaries -- Chapter 2: The geometry of blades -- Chapter 3: Examples with geometric algebra -- Chapter 4: Appendix -- 4.1. Construction of a geometric algebra -- References
