[constantcrying]

>What are the advantages of GA over regular linear algebra in practice?

It is a unified description of certain kinds of spaces. The greatest conceptual advantage over "regular linear algebra" (the quotes are there because you are still doing regular linear algebra, but with a different spaces and operations than R^n) is that it allows a very nice description of Euclidean space. Where e.g. points and rotations are the same type of object.

I think the best example are complex numbers. Complex numbers are just 2D vectors where multiplication is rotation. (Defining i as the square root of -1 is probably the worst way to think about complex numbers). The way they are doing it (the right way IMO) is actually as a 2^1 dimensional Vectorspace, with one multiplication (fully described by the product of all basis vectprs with one another) which describes the geometric properties of 2D euclidean space.

You can see more here: https://bivector.net/index.html

>Can you create better neural nets or faster graph search algorithms? What is the draw, computationally?

In one talk they claimed this is the case for graphical applications, where they contrasted it with Quarternions.

It is useless for neural nets, which need fast high dimensional matrix multiplication.