D. Klawitter: Reflections in conics, quadrics and hyperquadrics via Clifford algebra


Daniel Klawitter, Reflections in conics, quadrics and hyperquadrics via Clifford algebra, Beitr Algebra Geom (2016) 57:221–242, DOI 10.1007/s13366-014-0218-2, Received: 14 April 2014 / Accepted: 27 August 2014 / Published online: 10 September 2014. URL: http://link.springer.com/article/10.1007/s13366-014-0218-2

Abstract: In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal geometric algebra model is achieved. We discuss the geometric objects that can be represented. Furthermore,we show that the Pin group of this geometric algebra corresponds to the group of inversions with respect to quadrics in principal position. We discuss the construction for the two- and three-dimensional case in detail and give the construction for arbitrary dimension.

Keywords: Clifford algebra, Geometric algebra, Generalized inversion, Conic, Quadric, Hyperquadric.
Mathematics Subject Classfication: 15A66, 51B99, 51M15, 51N15

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