Exterior Calculus: Theory and Cases

Geometric Algebra on G3

Author(s): Carlos Polanco *

Pp: 31-47 (17)

DOI: 10.2174/9789814998789121010009

* (Excluding Mailing and Handling)


This chapter reviews and elaborates on the operators from Geometric algebra on G2 to G3. This algebra is attributed to Hermann Grassmann [Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik 1842]. It is formed by two main operators, the outer product and the inner product, it also includes the element called bivector. Here, we review their properties and their application in space.

Keywords: Associativity: a(bc) = (ab)c, bivector: a∧b, blades < a >, component: vk, component: v⊥, 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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