Transformation
From Encyclopedia of Mathematics
A mapping 
of a set 
(in general endowed with some structure) into itself. The image of an element 
under the transformation 
is denoted by 
, 
, 
, or 
. The set of all transformations of a set 
into itself forms a transformation semi-group with respect to multiplication (composition), which is called the symmetric transformation semi-group on 
. The invertible elements of this semi-group are called permutations (cf. Permutation of a set). All permutations on a set 
form a subgroup of the symmetric semi-group — the symmetric group.
See also Permutation group; Transformation group.
How to Cite This Entry:
Transformation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transformation&oldid=39298
Transformation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transformation&oldid=39298
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article