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Low Dimensional Geometric Algebras

  • Carlile Lavor
  • Sebastià Xambó-Descamps
  • Isiah Zaplana
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

The concept of geometric algebra (GA) arises out of the desire to multiply vectors with the usual rules of multiplying numbers, including the usual rules for taking inverses. From that point of view, the construction of GA is an instance of a powerful mechanism used in mathematics that may be described as creating virtue out of necessity. In general, this mechanism comes to the rescue when the need arises to extend a given structure in order to include desirable features that are not present in that structure.

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Copyright information

© The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Carlile Lavor
    • 1
  • Sebastià Xambó-Descamps
    • 2
  • Isiah Zaplana
    • 3
  1. 1.Department of Applied Maths (IMECC-UNICAMP)University of CampinasCampinasBrazil
  2. 2.Departament de MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Institut d’Org. i Control de Sist. Ind.Universitat Politècnica de CatalunyaBarcelonaSpain

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