[thomaskoopman]

Yes, but quaternions of unit length are a representation of the rotation group in 3D space ( https://en.wikipedia.org/wiki/Representation_theory_of_SU(2)... ), which is how they are used for rotations.

[suspended_state]

The original question was: can quaternions be used in place of matrices to perform LLMs tasks, and the answer is: quaternions are 4 dimensions, with the implied meaning that matrices can cover different dimentionalities, which are needed for LLMs (and neural network in general).

[eru]

Yes, if you have essentially 4d objects and you disable 1 dimension by requiring unit length, you end up with something that is effectively 3d.

Of course, that the 3d thing you end up with represents rotations in 3d space is extremely neat; and not something all 3d things do.