- GA tends to attract a lot of crackpot. In fact most mathematicians avoid the name Geoemtric algebra and call it Clifford algebra to disassociate with them.
- Most of the usefulness of GA comes from just exterior algebra and exterior product/wedge product is more important than geometric product.
- It shows up in spinor field in physics but this does not concern most people that do not work in quantum physics.
My rudimentary view towards GA:
- It is useful in game physics since rotors can represent n-dimensional rotation in 2^{n-1} numbers instead of n^2 numbers as 2^{n-1} < n^2 when n <= 6. You can use PGA if you want to add translation as well. It is also better in interpolation.
- Outside of this you should just probably just learn exterior algebra instead.
TLDR:
- GA tends to attract a lot of crackpot. In fact most mathematicians avoid the name Geoemtric algebra and call it Clifford algebra to disassociate with them.
- Most of the usefulness of GA comes from just exterior algebra and exterior product/wedge product is more important than geometric product.
- It shows up in spinor field in physics but this does not concern most people that do not work in quantum physics.
My rudimentary view towards GA:
- It is useful in game physics since rotors can represent n-dimensional rotation in 2^{n-1} numbers instead of n^2 numbers as 2^{n-1} < n^2 when n <= 6. You can use PGA if you want to add translation as well. It is also better in interpolation.
- Outside of this you should just probably just learn exterior algebra instead.