Active and passive transformation: Difference between revisions

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Spatial transformations in the Euclidean space \R^3: Avoid math tags in section headings per Help:Displaying a formula#LaTeX vs. {{math}}. Currently causes TOC to display UNIQ...QINU (phab:T295430)
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which can be viewed either as an ''active transformation'' or a ''passive transformation'' (where the above [[matrix (mathematics)|matrix]] will be [[inverse matrix|inverted]]), as described below.
 
==Spatial transformations in the Euclidean space R<mathsup>\R^3</mathsup>==
In general a spatial transformation <math>T\colon\R^3\to \R^3</math> may consist of a translation and a linear transformation. In the following, the translation will be omitted, and the linear transformation will be represented by a 3×3 matrix <math>T</math>.