Might be worth pointing out that quaternions themselves are often represented as matrices as well: That’s the Pauli matrices, widely used to model quantum spin.

Might be worth pointing out that quaternions themselves are often represented as matrices as well: That’s the Pauli matrices, widely used to model quantum spin. One advantage of quaternions is that it’s (IMO) easier to calculate things with them using only pen and paper than it is to do equivalent matrix multiplications by hand. Personally I find them “intuitive” in the same sense as complex numbers are intuitive: They seemed weird on first exposure, but they now feel simpler to use and reason about than the alternatives I know.