Active and passive transformation: Difference between revisions

m (clean up and regexp typo fixing, typo(s) fixed: ie. → i.e. using AWB)
:<math>v'^a=(R^{-1})_b^a v^b</math>
so that
:<math>\mathbf{v}=v'^a\mathbf{e}'_a=v^b(R^{-1})_b^a R_a^c \mathbf{e}_c=v^b\delta^c_b \mathbf{e}_c=v^b\mathbf{e}_b.</math>
Thus, in order for the vector to remain unchanged by the passive transformation, the coordinates of the vector ''must'' transform according to the inverse of the active transformation operator.<ref name=Amidror>