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== Example ==
[[File:
[[File:Alias and alibi transformations 1 en.png|thumb|upright=1.8|Translation and rotation as passive (''alias'') or active (''alibi'') transformations]]
As an example, let the vector <math>\mathbf{v}=(v_1,v_2) \in \R^2</math>, be a vector in the plane. A rotation of the vector through an angle ''θ'' in counterclockwise direction is given by the [[rotation matrix]]:
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