Abstract
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
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
On Generalized Growth rates of Integer Translated Entire and Meromorphic Functions
Introductory Statistics
Advanced Mathematical Applications in Data Science
Advanced Calculus - Fundamentals of Mathematics
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
Advances in Time Series Forecasting
Advances in Time Series Forecasting
Current Developments in Mathematical Sciences
Current Developments in Mathematical Sciences