On the other hand, when one views T as a passive transformation, the initial vector v = ( v x , v y , v z ) is left unchanged, while the coordinate system and its basis vectors are transformed in the opposite direction, that is, with the inverse transformation T − − 1 . This gives a new coordinate system XYZ with basis vectors: e X = T − − 1 ( 1 , 0 , 0 ) , e Y = T − − 1 ( 0 , 1 , 0 ) , e Z = T − − 1 ( 0 , 0 , 1 )