Making derived products out of the geometric product requires care in consistency. We show how a split based on outer product and scalar product necessitates a slightly different inner product than usual. We demonstrate the use and geometric significance of this contraction, and show how it simplifies treatment of meet and join. We also derive the sufficient condition for covariance of expressions involving outer and inner products.


Covariance Univer Hone 


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  1. [1]
    T.A. Bouma, From Unoriented Subspaces to Blade Operators, Chapter 4 in this volume.Google Scholar
  2. [2]
    L. Dorst, Honing geometric algebra for its use in the computer sciences. In Geometric Computing with Clifford Algebra (G. Sommer, ed.), Springer, 2001. Preprint available at http://www.science.uva.nl/~leo/clifford/Google Scholar
  3. [3]
    L.Dorst, S.Mann, T.A.Bouma, GABLE: A Geometric AlgeBra Learning Environment, www. science.uva.nl/~leo/clifford/gable.htmlGoogle Scholar
  4. [4]
    D. Hestenes and G Sobczyk, Clifford Algebra to Geometric Calculus, D. Reidel, Dordrecht, 1984.MATHGoogle Scholar
  5. [5]
    P. Lounesto, Marcel Riesz’s work on Clifford algebras. In Clifford Numbers and Spinors (E.F. Bolinder and P. Lounesto, eds.), Kluwer Academic Publishers, pp. 215–241, 1993.Google Scholar
  6. [6]
    L. Svensson, Personal communication at ACACSE’99, Ixtapa, Mexico.Google Scholar
  7. [7]
    J. Stolfi, Oriented Projective Geometry, Academic Press, 1991.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Leo Dorst

There are no affiliations available

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