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.
Example Usage of transformation
andiepetoskey: Changing the way people learn. Changing the way people earn. Creating transformation around the world. http://budurl.com/ilgtrain
cindygolding: @CoryBooker ~ Let's learn from snow flakes: individually each is beautiful yet fragile, together they're a powerful force of transformation.
kaijson: RT @CoryBooker: Let's learn from snow flakes: individually each's beautiful yet fragile, togther they're a powerful force of transformation.