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- Group_representation abstract "In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well-understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system. 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 "representation" means a homomorphism from the group to the automorphism group of an object. If the object is a vector space we have a linear representation. Some people use realization for the general notion and reserve the term representation for the special case of linear representations. The bulk of this article describes linear representation theory; see the last section for generalizations.A representation should not be confused with a presentation.".
- Group_representation wikiPageID "12695".
- Group_representation wikiPageRevisionID "579120420".
- Group_representation hasPhotoCollection Group_representation.
- Group_representation subject Category:Group_theory.
- Group_representation subject Category:Representation_theory.
- Group_representation subject Category:Representation_theory_of_groups.
- Group_representation comment "In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well-understood.".
- Group_representation label "Darstellungstheorie (Gruppentheorie)".
- Group_representation label "Groepsrepresentatie".
- Group_representation label "Group representation".
- Group_representation label "Rappresentazione dei gruppi".
- Group_representation label "Representación de grupo".
- Group_representation label "Representação de grupo".
- Group_representation label "Reprezentacja grupy".
- Group_representation label "Représentation de groupe".
- Group_representation label "Представление группы".
- Group_representation label "نظرية التمثيل".
- Group_representation label "群の表現".
- Group_representation label "群表示論".
- Group_representation sameAs Reprezentace_(grupa).
- Group_representation sameAs Darstellungstheorie_(Gruppentheorie).
- Group_representation sameAs Representación_de_grupo.
- Group_representation sameAs Représentation_de_groupe.
- Group_representation sameAs Rappresentazione_dei_gruppi.
- Group_representation sameAs 群の表現.
- Group_representation sameAs 군_표현론.
- Group_representation sameAs Groepsrepresentatie.
- Group_representation sameAs Reprezentacja_grupy.
- Group_representation sameAs Representação_de_grupo.
- Group_representation sameAs m.03bcp.
- Group_representation sameAs Q1055807.
- Group_representation sameAs Q1055807.
- Group_representation wasDerivedFrom Group_representation?oldid=579120420.
- Group_representation isPrimaryTopicOf Group_representation.