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Representation (mathematics)
In mathematics, representation is a very general relationship that expresses similarities between objects. Roughly speaking, a collection ''Y'' of mathematical objects may be said to ''represent'' another collection ''X'' of objects, provided that the properties and relationships existing among the representing objects ''yi'' conform in some consistent way to those existing among the corresponding represented objects ''xi''. Somewhat more formally, for a set ''Π'' of properties and relations, a ''Π''-representation of some structure ''X'' is a structure ''Y'' that is the image of ''X'' under a homomorphism that preserves ''Π''. The label ''representation'' is sometimes also applied to the homomorphism itself.
== Representation theory ==
Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representing of elements of algebraic structures by linear transformations of vector spaces.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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