Geometric (Clifford) algebra and its applications
| dc.creator | Lundholm, Douglas | |
| dc.date | 2006-05-10 | |
| dc.date.accessioned | 2026-07-07T10:16:35Z | |
| dc.date.available | 2026-07-07T10:16:35Z | |
| dc.description | In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional approach. Furthermore, I give a quick review of classic results regarding geometric algebras, such as their classification in terms of matrix algebras, the connection to orthogonal and Spin groups, and their representation theory. A number of lower-dimensional examples are worked out in a systematic way using so called norm functions, while general applications of representation theory include normed division algebras and vector fields on spheres. I also consider examples in relativistic physics, where reformulations in terms of geometric algebra give rise to both computational and conceptual simplifications. | |
| dc.description | M.Sc. Thesis (January 2006), 68 pages. Department of Mathematics, Royal Institute of Technology, Sweden | |
| dc.identifier | https://arxiv.org/abs/math/0605280 | |
| dc.identifier | http://arxiv.org/abs/math/0605280 | |
| dc.identifier | Trita-MAT. MA, ISSN 1401-2278; 2006:01 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173556 | |
| dc.subject | Rings and Algebras | |
| dc.title | Geometric (Clifford) algebra and its applications | |
| dc.type | text |