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Introduction to Geometric Algebra

  • Eduardo Bayro-CorrochanoEmail author
Chapter
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Abstract

This chapter gives a detailed outline of geometric algebra and explains the related traditional algebras in common use by mathematicians, physicists, computer scientists, and engineers.

References

  1. 1.
    Needham, T. (2003). Visual analysis, complex. New York: Oxford University Press. Reprinted.Google Scholar
  2. 2.
    Li, H., Hestenes, D., & Rockwood, A. (2001). Generalized homogeneous coordinates for computational geometry. In G. Sommer (Ed.), Geometric computing with Clifford algebra (pp. 27–59). New York: Springer-Verlag.CrossRefGoogle Scholar
  3. 3.
    Grassmann, H. (1877). Der Ort der Hamilton’schen Quaternionen in der Ausdehnungslehre. Mathematische Annalen, 12, 375.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Clifford, W. K. (1878). Applications of Grassmann’s extensive algebra. American Journal of Mathematics, 1, 350–358.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hestenes, D. (1966). Space-time algebra. London: Gordon and Breach.zbMATHGoogle Scholar
  6. 6.
    Hestenes, D., & Sobczyk, G. (1984). Clifford algebra to geometric calculus: A unified language for mathematics and physics. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  7. 7.
    Hestenes, D. (1986). New foundations for classical mechanics. Dordrecht: D. Reidel.CrossRefGoogle Scholar
  8. 8.
    Hestenes, D., & Ziegler, R. (1991). Projective geometry with Clifford algebra. Acta Applicandae Mathematicae, 23, 25–63.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bayro-Corrochano, E. (2018). Geometric algebra applications vol. I computer vision, graphics and neurocomputing. Springer Verlag.Google Scholar
  10. 10.
    Doran, C., & Lasenby, A. (2005). Geometric algebra for physicists. Cambridge University Press.Google Scholar
  11. 11.
    Lounesto, P. (1997). Clifford algebras and spinors. Cambridge: Cambridge University Press.zbMATHGoogle Scholar
  12. 12.
    Hestenes, D. (1991). The design of linear algebra and geometry. Acta Applicandae Mathema ticae, 23, 65–93.Google Scholar
  13. 13.
    Lounesto, P. (1987). CLICAL software packet and user manual. Helsinki University of Technology of Mathematics, Research report A248.Google Scholar
  14. 14.
    Perwass, C. B. U. (2006). CLUCal. http://www.clucal.info/.
  15. 15.
    Ablamowicks R. eCLIFFORD Software packet using Maple for Clifford algebra. Computations. http://math.tntech.edu/rafal.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Electrical Engineering and Computer Science DepartmentCINVESTAVGuadalajaraMexico

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