Active And Passive Transformation
In the physical sciences, an active transformation is one which actually changes the physical position of a system, and makes sense even in the absence of a coordinate system whereas a passive transformation is a change in the coordinate description of the physical system (change of basis). The distinction between active and passive transformations is important. By default, by transformation, mathematicians usually mean active transformations, while physicists could mean either.
Put differently, a passive transformation refers to observation of the same event from two different coordinate frames. On the other hand, the active transformation is a new mapping of all points from the same coordinate frame. If we describe successive displacements of a rigid body, the active transformation is useful. If we describe the displacements of individual arms of a robot, each with its own coordinate frame, the passive interpretation is useful to depict all the arm displacements from a common perspective.
Read more about Active And Passive Transformation: Example
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