How can I do this when the multiplication between two Hurwitz quaternions can give you a non Hurwitz quaternion (eg 1+2.25i+2.5j+3.75k)?
I can do it for Lipschitz quaternions, but not when the values can be half.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos May 17 '19 at 12:35
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You must have miscomputed, as the product of Hurwitz quaternions is also a Hurwitz quaternion: https://en.wikipedia.org/wiki/Hurwitz_quaternion – Kimball May 17 '19 at 13:21