Chapter 15. Alternative Ways of Writing Quaternions
We have taken advantage so far of the clarity of a notation in which a quaternion is represented simply as a four-vector—a list of four variables that obeys certain rules. There are several other completely equivalent notations, including Hamilton’s original formulas, that incorporate the rules of quaternion multiplication as an intrinsic part of the notation itself. As far as we are concerned, these add no new information to the notation we have been using and thus they are not essential to the overall problem of trying to visualize quaternions. Nevertheless, they do relate to notations used in other fields of mathematics and physics and thus have value for their ability to expose those connections. ...
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