Abstract
The aim of this chapter is to introduce the geometric algebra of a quadratic space (E, q) by following an axiomatic approach. The root idea is to explore how to minimally enrich the structure (E, q) so that vectors can be multiplied with the usual rules of an algebra, and that non-isotropic vectors can be inverted.
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References
E. Artin, Geometric Algebra. Tracts in Pure and Applied Mathematics, vol. 3 (Interscience Publishers, New York, 1957)
M. Riesz, Clifford Numbers and Spinors. Fundamental Theories of Physics, vol. 54 (Kluwer Academic Publishers, Dordrecht, 1997). An edition by E.F. Bolinder and P. Lounesto of M. Riesz Clifford numbers and spinors. Lecture Series No. 38k Institute for Fluid Dynamics and Applied Mathematics, University of Maryland (1958)
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Xambó-Descamps, S. (2018). Geometric Algebra. In: Real Spinorial Groups. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-00404-0_3
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DOI: https://doi.org/10.1007/978-3-030-00404-0_3
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