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(Simplifying. Using "coordinate system" rather than "coordinate frame". The most usual expressions are "reference frame", "coordinate system", "basis". Coordinate frame is less frequently used.) 
(Also known as alibi and alias transformations) 

[[File:PassiveActive.JPGthumb310pxIn 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 are the same as the coordinates of P relative to the rotated coordinate system.]]
In
Put differently, a ''passive'' transformation refers to observation of the ''same'' event from two different coordinate systems.<ref name= Davidson>
