[[File:PassiveActive.JPG|thumb|310px|In the active transformation (left), a point moves from position P to P' by rotating clockwise by an angle θ about the origin of the coordinate system. In the passive transformation (right), point P does not move, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P' in the active case (i.e. relative to the original coordinate system) are the same as the coordinates of P relative to the rotated coordinate system.]]
In [[physics]] and [[engineering]], an '''active transformation''', or '''alibi transformation''', is a [[Transformation (mathematics)|transformation]] which actually changes the physical position of a point, or [[rigid body]], which can be defined even in the absence of a [[coordinate system]]; whereas a '''passive transformation''', or '''alias transformation''', is merely a change in the coordinate system in which the object is described (change of coordinate map, or [[change of basis]]). By default, by ''transformation'', [[mathematician]]s usually refer to active transformations, while [[physicist]]s and [[engineer]]s could mean either.
Put differently, a ''passive'' transformation refers to description of the ''same'' object in two different coordinate systems.<ref name= Davidson>