# Geometric transformation

In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both ${\displaystyle \mathbb {R} ^{2}}$ or both ${\displaystyle \mathbb {R} ^{3}}$ — such that the function is injective so that its inverse exists.[1] The study of geometry may be approached via the study of these transformations.[2]