Group representation

Representation theory is the branch of mathematics that studies properties of abstract groups via their representations as linear transformations of vector spaces. Representation theory is important because it enables many group-theoretic problems to be reduced to problems in linear algebra, which is a very well-understood theory.

Related Topics:
Mathematics - Groups - Linear transformation - Vector space - Group-theoretic - Linear algebra

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The term representation of a group is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical object. More formally, a "description" means a homomorphism from the group to the automorphism group of the object. If the object is a vector space we have a linear representation. Some people use realization for this notion and reserve the term representation for linear representations. The bulk of this article describes linear representation theory; see the last section for generalizations.

Related Topics:
Homomorphism - Automorphism group

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