An active transformation is one which actually changes the physical state of a system and makes sense even in the absence of a coordinate system whereas a passive transformation is merely a change in the coordinate system of no physical significance. The distinction between active and passive transformations is one which should always be kept in mind when working with transformations. By default, by transformation,mathematicians usually mean active transformations, while physicists could mean either.
This article is a stub. You can help Wikipedia by fixing it.
