Post #2342910

@mathemagical@mathstodon.xyz Yeah, I started with a lie group, but if I use exp(log(A)+log(B)) as a commutative stand-in for the multiplication operation then I think it's a proper algebra. Still a lot of trig functions, but I can make the matrices behave properly. Also, If I only use real numbers in the key and query matrices and then replace the dot product with a more generic angle difference function that generates reals then I only have to raise quaternions to real powers. No quat^quat is ever required. Also rotatary position encoding is trivial because it's all already rotations 🤣 .