Coincidentally, this conference talk[1] released yesterday regarding vector multiplication. In it, it describes how quaternions can be seen as an extension of 3

Coincidentally, this conference talk[1] released yesterday regarding vector multiplication. In it, it describes how quaternions can be seen as an extension of 3d vector spaces, like how complex numbers can be seen as an extension to 2d vector spaces. More specifically, quaternions are a 4d vector with the basis of {1,yz,xz,xy} where those "bivectors" result from 3d vector multiplication, e.g. (ax+by+cz)(dx+ey+fz) [1]: https://youtu.be/htYh-Tq7ZBI https://youtu.be/htYh-Tq7ZBI