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=== Passive transformation ===
On the other hand, when one views
:<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
:<math>(v'_1,v'_2)=R
so that the coordinates of the vector ''must'' transform according to the inverse of the active transformation
{{cite book isbn=1402054572 year=2007 publisher=Springer title=The theory of the Moiré phenomenon: Aperiodic layers first=Isaaclast=Amidror

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