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Rotation in nD<br />
Consider: R v R -1 mit v =v ┴ + v ║ :<br />
– We have: U v ┴ = 0 d.h. Uv ┴ =U v ┴<br />
=u 1 u 2 v ┴= - u 1 v ┴ u 2= v ┴ u 1 u 2= v ┴ U =v ┴U<br />
i.e. v ┴ commutes with U, thus also R<br />
R v R -1 = R v ┴ R -1 + R v ║ R -1<br />
R v ┴ R -1 =(cos + sin U) v ┴ (cos - sin U)<br />
= v ┴(cos² - sin² U²) = v ┴<br />
R v R-1 = v┴ + e U v║ e- U = v┴ + v║ e-2 U<br />
Rotation<br />
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