Active and passive transformation: Difference between revisions

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=== 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:
:<math>\mathbf{v}=(v_1,v_2)=v'_1R^*(1,0)+v'_2R*^(0,1)=R^*(v'_1,v'_2)</math>.
From this equation one sees that the new coordinates (that is, coordinates with respect to the new basis) are given by