For a mathematician, how is rotation defined in the most general sense?(adsbygoogle = window.adsbygoogle || []).push({});

Question arose to me because it occured to me that an essential property of the rotation matrix is that it preserves lengths. Is this the only mapping (if not please give me a counterexample) that has this property (identity is also a special case of a rotation of course) and can this be shown?

Might seem like a very lose question and indeed it is, so speak freely about anything that you think could improve my understanding of the fundamental mathematics behind rotation.

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# Rotation matrix

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