Advanced Calculus - Fundamentals of Mathematics

Geometric Algebra

Author(s): Carlos Polanco

Pp: 124-138 (15)

DOI: 10.2174/9789811415081119010015

* (Excluding Mailing and Handling)


This chapter intends to be a survey on Exterior Algebra. This algebra is attributed to Hermann Grassmann [Die lineare Ausdehnungslehre, ein neuer Zweig der Mathematik, 1842], and it is formed by two operators: the exterior product and inner product. William K. Clifford unified both products under the geometric product operator and David Hestenes improved the geometric and computer aspects of Geometric algebra. Here, we review the main operators and their properties, as well as their application in the representation of lines and planes.

Keywords: Bivector, Differential forms, Differentiation, Dot product, Dual space, Exterior product, Geometric algebra, Geometric product, Grassmann algebra, Inner product, Norm, Oriented plane, Orthogonal basis, Reflections, Rigid body motions, Rotations.

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