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 directondirection, 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, according to:
From this equation one sees that the new coordinates (that is, coordinates with respect to the new basis) are given by