Geometric Algebra

Did you know that the inner product space R n can be embedded in a vector space of dimension 2 n which is also an associative algebra with unit, the geometric algebra?

Some members of the geometric algebra represent geometric objects in R n . Other members represent geometric operations on the geometric objects.

Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective geometry. They provide a unified mathematical language for physics (classical and quantum mechanics, electrodynamics, relativity), the geometrical aspects of computer science (e.g., graphics, robotics, computer vision), and engineering.