Active and passive transformation: Difference between revisions

(→‎See also: Inserted Rotation of axes and Translation of axes)
== Example ==
 
As an example, in the vector space ℝ<sup>2</sup>, let {'''e'''<sub>1</sub>,'''e'''<sub>2</sub>} be a [[basis (linear algebra)|basis]], and consider the vector '''v''' = ''v''<sup>1</sup>'''e'''<sub>1</sub> + ''v''<sup>2</sup>'''e'''<sub>2</sub>. A rotation of the vector through angle θ is given by the matrix:
:<math>R=
\begin{pmatrix}
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