Active and passive transformation: Difference between revisions

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Upgrade "Alibi and alias rotations" image from a PNG to an SVG.
Undid revision 1238233918 by Davidvandebunte (talk) either png or svg is fine, but the previous image was more legible, with clearer color coding. the numbers weren't necessary before but the square roots etc. are gratuitous and distracting
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== Example ==
[[File:AlibiAlias and aliasalibi rotations.svgpng|thumb|upright=1.8|Rotation considered as ana activepassive (''alibialias'') or passiveactive (''aliasalibi'') transformation]]
[[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]]: