Exterior Calculus: Theory and Cases

Geometric Algebra on G2

Author(s): Carlos Polanco *

Pp: 14-30 (17)

DOI: 10.2174/9789814998789121010008

* (Excluding Mailing and Handling)


This chapter is a review of Geometric algebra or Grassmann alge- bra on G2. This algebra is attributed to Hermann Grassmann [Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik 1842]. It has two main operators: outer product and inner product. Here, we will also study dot product, and geometric product, as well as their properties. We will start with the definition of Geometric algebra, its properties and most useful tools.With this background, we will define the differential forms in Chap. 5.

Keywords: Associativity: a(bc) = (ab)c, bivector, blades < a >i, distributivity: a(b+c), distributivity: a∧(b+c), dual Iar = bn−r, equation of a line, outer product, geometric algebra, geometric product, inner product, lines, multiplicative inverse: a−1, norm ||a||, reflections, reversion: a†, rotations

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