User talk:11wx

On the Wikipedia page: Quaternions and Spatial Rotations[1], in the section "Using quaternions as rotations", you inserted the comment: { Note that q and −q represent the same rotation, and the mapping from unit quaternions to three-dimensional rotations is two-to-one.}

I think the point you raised is important, and deserved both a proof and a discussion of the geometric reasons for and implications of the two-to-one mapping.

So - I expanded it and moved it below the conjugation equation, since the fact that the conjugation equation is quadratic in q, makes it clear that conjugation by q and by −q provide the same transformation.

Macchess (talk) 05:24, 13 December 2022 (UTC)

[1] https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation Macchess (talk) 05:24, 13 December 2022 (UTC)