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