Geometric algebra

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Geometric Algebra a.k.a. Clifford Algebra (Wikipedia)

IMHO, the most powerful, useful, under-appreciated, and fascinating invention in mathematics in the last 100 years

Resources

• Geometric Algebra Primer - the original by Jaap Suter PDF | Scribd

"Adopted with great enthusiasm in physics, geometric algebra slowly emerges in computational science. Its elegance and ease of use is unparalleled. By introducing two simple concepts, the multivector and its geometric product, we obtain an algebra that allows subspace arithmetic. It turns out that being able to ‘calculate’ with subspaces is extremely powerful, and solves many of the hacks required by traditional methods. This paper provides an introduction to geometric algebra. The intention is to give the reader an understanding of the basic concepts, so advanced material becomes more accessible."

• Lomont's collection of GA papers