#ericchisolm — Public Fediverse posts

This is an introduction to #GeometricAlgebra, an alternative to traditional #VectorAlgebra that expands on it in two ways:
1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension.
2. It defines a product that’s strongly motivated by #geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane.

This system was invented by #WilliamClifford and is more commonly known as #CliffordAlgebra. It’s actually older than the #VectorAlgebra that we use today (due to #Gibbs) and includes it as a subset. Over the years, various parts of #CliffordAlgebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that #GeometricAlgebra, not the reduced version we use today, deserves to be the standard “vector algebra.” My goal in these notes is to describe #GeometricAlgebra from that standpoint and illustrate its usefulness. The notes are work in progress; I’ll keep adding new topics as I learn them myself.