In this video, I introduce some of the concepts of geometric (Clifford) algebra, focusing on two-dimensional space (R^2). We'll talk about the wedge (exterior) product, review the dot product, and introduce the geometric product. We'll see that a new mathematical object, the bivector, arises from considering the wedge product. Furthermore, we're going to see that this bivector behaves like an imaginary unit in that it squares to -1. Since it has this property, it naturally relates to vector rotation in 2D, like the complex numbers.
Recommended video on Clifford algebra:
https://www.youtube.com/watch?v=rqadK8-dN-Y
...and other video series covering Geometric Algebra (Nick Okamoto): https://www.youtube.com/watch?v=P-IKemH3jsg&list=PLQ6JJNfj9jD_H3kUopCXkvvGoZqzYOzsV