Exterior Calculus: Theory and Cases

Geometric Algebra on Gn

Author(s): Carlos Polanco *

Pp: 48-59 (12)

DOI: 10.2174/9789814998789121010010

* (Excluding Mailing and Handling)


This chapter reviews and elaborates on the operators of Geometric algebra from G3 to Gn. 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 inner product. Here, a new element is introduced the multivector, we review these operators, their properties, and their application in the representation of curves, planes, and objects on space Gn.

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, multivector a∧b∧c∧···∧z, norm ||a||, reflections, reversion: a†, rotations, trivector: a∧b∧c

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