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Most often the multiplication in convention descriptions and papers is described in matrix multiplication style like this: q · p := Q(q)p Q(q) := [q0 −q1 −q2 −q3] [q1 q0 −q3 q2] [q2 q3 q0 −q1] [q3 −q2 q1 q0] I'm just rearanging the terms such that it's easily comparable with these definitions additional to it being clearly described by documenting we use the hamilton convention.