Quaternion relative error measurement
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So, for the last couple of days I have been trying to implement different means of data compression, primarily related to algebraic entities. In order to evaluate the result (primarily precision loss) I have been relying on calculating the relative error.

Now, doing so for standard linear algebra constructs such as a matrix or vector is no problem but I have run into somewhat of a snag when it comes to quaternions. Is there a standard measurement of relative error when it comes to quaternions? Now I am forced to convert the quaternions to matrices and calculate their relative error... which isn't really the same thing.

Would it be viable to adapt the standard vector approach to quaternions?.. seeing as they are kind of like 4D vectors?

Any thoughts on this would be welcome! :)
-Maigo 