Transform (mathematics) | Wikipedia audio article
0This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Transformation_(function)
00:00:53 1 Translation
00:01:46 2 Reflection
00:02:12 3 Glide reflection
00:03:05 4 Rotation
00:03:32 5 Scaling
00:04:25 6 Shear
00:05:18 7 More generally
00:06:11 7.1 Partial transformations
00:07:05 8 Algebraic structures
00:07:58 9 Combinatorics
00:08:51 10 See also
00:09:44 11 References
00:10:37 Algebraic structures
00:11:30 Combinatorics
00:12:23 See also
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SUMMARY
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In mathematics, particularly in semigroup theory, a transformation is a function f that maps a set X to itself, i.e. f : X → X. In other areas of mathematics, a transformation may simply be any function, regardless of domain and codomain. This wider sense shall not be considered in this article; refer instead to the article on function for that sense.
Examples include linear transformations and affine transformations, rotations, reflections and translations. These can be carried out in Euclidean space, particularly in R2 (two dimensions) and R3 (three dimensions). They are also operations that can be performed using linear algebra, and described explicitly using matrices.