In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. 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. More specifically, given 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 (such as group homomorphism in group theory).[1][2]
- ^ Weisstein, Eric W. "Group Representation". mathworld.wolfram.com. Retrieved 2019-12-07.
- ^ Teleman, Constantin. "Representation Theory" (PDF). math.berkeley.edu. Retrieved 2019-12-07.