In mathematics, a rule for changing a geometric figure or algebraic expression into another, usually accompanied by a rule for transforming it back. In geometry and topology, a transformation (e.g., flipping horizontally or vertically, rotating, or stretching vertically or horizontally) moves each point in a figure or graph to another position. A graph also undergoes a transformation when its coordinate system is changed.
For example, the equations that establish a correspondence between the rectangular and polar coordinate systems constitute a transformation. In analysis, a transformation is a procedure that changes one function into another. Of special interest in many fields of mathematics are transformations forming a group, in which any two transformations applied successively produce the same result as another transformation in the group and each transformation has an inverse transformation (which undoes it) in the group. &Seealso; group theory, integral transform, linear transformation.
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