03 November ~ N. Carr “Geometric algebra- how to multiply vectors properly.”

A geometric algebra is a real vector space endowed with the geometric product, which contains the familiar dot product and a generalisation of the cross product. Geometric algebras crop up in many familiar guises, such as the complex numbers, quaternions, and spinors. They also encode reflections and rotations in an elegant fashion, without the use of matrices. Lastly, we can also use them to define a vector derivative, which allows for an elegant reformulation of the theory of complex analytic functions, and various important equations in physics, like Maxwell’s equations.”