Active and passive transformation: Difference between revisions

=== Passive transformation ===
On the other hand, when one views ''<math>R''</math> as a passive transformation, the initial vector '''v''' is left unchanged, while the coordinate system and its basis vectors are rotated in the opposite directon, i.e. with the rotation <math>R^{-1}=R^*</math>. In order for the vector to remain fixed, the coordinates in terms of the new basis must change., Foraccording ato: counterclockwise rotation of coordinate systems:
From this equation one sees that the new coordinates (that is, coordinates with respect to the new basis) are given by
so that the coordinates of the vector ''must'' transform according to the inverse of the active transformation operatorof the coordinate system.<ref name=Amidror>
{{cite book |isbn=1-4020-5457-2 |year=2007 |publisher=Springer |title=The theory of the Moiré phenomenon: Aperiodic layers |first=Isaac|last=Amidror