Abstract
The structures of matrix algebra and geometric algebra are completely compatible and in many ways complimentary, each having their own advantages and disadvantages. We present a detailed study of the hybrid 2 × 2 matrix geometric algebra M(2,IG) with elements in the 8 dimensional geometric algebra IG=IG 3 of Euclidean space. The resulting hybrid structure, isomorphic to the geometric algebra IG 4,1 of de Sitter space, combines the simplicity of 2× 2 matrices and the clear geometric interpretation of the elements of IG. It is well known that the geometric algebra IG(4,1) contains the 3-dimensional affine, projective, and conformal spaces of Möbius transformations, together with the 3-dimensional horosphere which has attracted the attention of computer scientists and engineers as well as mathematicians and physicists. In the last section, we describe a sophisticated computer software package, based on Wolfram’s Mathematica, designed specifically to facilitate computations in the hybrid algebra.
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© 2005 Springer-Verlag Berlin Heidelberg
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Sobczyk, G., Erlebacher, G. (2005). Hybrid Matrix Geometric Algebra. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_16
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DOI: https://doi.org/10.1007/11499251_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26296-1
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