College - Author 1
College of Engineering
Department - Author 1
Aerospace Engineering Department
Degree Name - Author 1
BS in Aerospace Engineering
Eric Mehiel, College of Engineering, Aerospace Engineering Department
The goals of this paper are to provide an introduction to vector, exterior and Clifford algebra and to present a method for performing Clifford algebra calculations efficiently using representation theory. Vectors, exterior algebra and other mathematical and historical foundations of Clifford algebra are introduced. Matrix representations of Clifford algebras are elucidated. The computation of rotations using Clifford representations of spin groups is discussed, and a few of the relevant scientific and engineering applications of the Clifford and exterior algebras are noted throughout.