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- Character_group abstract "In mathematics, a character group is the group of representations of a group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory. Whenever a group is represented by matrices, the function defined by the trace of the matrices is called a character; however, these traces do not in general form a group. Some important properties of these one-dimensional characters apply to characters in general: Characters are invariant on conjugacy classes. The characters of irreducible representations are orthogonal.The primary importance of the character group for finite abelian groups is in number theory, where it is used to construct Dirichlet characters. The character group of the cyclic group also appears in the theory of the discrete Fourier transform. For locally compact abelian groups, the character group (with an assumption of continuity) is central to Fourier analysis.".
- Character_group wikiPageID "1384568".
- Character_group wikiPageLength "4510".
- Character_group wikiPageOutDegree "25".
- Character_group wikiPageRevisionID "681674528".
- Character_group wikiPageWikiLink Abelian_group.
- Character_group wikiPageWikiLink Category:Group_theory.
- Character_group wikiPageWikiLink Category:Number_theory.
- Character_group wikiPageWikiLink Category:Representation_theory_of_groups.
- Character_group wikiPageWikiLink Character_(mathematics).
- Character_group wikiPageWikiLink Character_theory.
- Character_group wikiPageWikiLink Complex_number.
- Character_group wikiPageWikiLink Conjugacy_class.
- Character_group wikiPageWikiLink Conjugate_transpose.
- Character_group wikiPageWikiLink Cyclic_group.
- Character_group wikiPageWikiLink Dirichlet_character.
- Character_group wikiPageWikiLink Discrete_Fourier_transform.
- Character_group wikiPageWikiLink Fourier_analysis.
- Character_group wikiPageWikiLink Function_(mathematics).
- Character_group wikiPageWikiLink Group_(mathematics).
- Character_group wikiPageWikiLink Group_homomorphism.
- Character_group wikiPageWikiLink Group_representation.
- Character_group wikiPageWikiLink Kronecker_delta.
- Character_group wikiPageWikiLink Mathematics.
- Character_group wikiPageWikiLink Matrix_(mathematics).
- Character_group wikiPageWikiLink Number_theory.
- Character_group wikiPageWikiLink Pontryagin_duality.
- Character_group wikiPageWikiLink Root_of_unity.
- Character_group wikiPageWikiLink Trace_(linear_algebra).
- Character_group wikiPageWikiLinkText "character group".
- Character_group wikiPageWikiLinkText "character".
- Character_group wikiPageWikiLinkText "characters".
- Character_group wikiPageWikiLinkText "non-principal character".
- Character_group wikiPageUsesTemplate Template:Apostol_IANT.
- Character_group subject Category:Group_theory.
- Character_group subject Category:Number_theory.
- Character_group subject Category:Representation_theory_of_groups.
- Character_group hypernym Group.
- Character_group type Band.
- Character_group type Field.
- Character_group comment "In mathematics, a character group is the group of representations of a group by complex-valued functions. These functions can be thought of as one-dimensional matrix representations and so are special cases of the group characters that arise in the related context of character theory. Whenever a group is represented by matrices, the function defined by the trace of the matrices is called a character; however, these traces do not in general form a group.".
- Character_group label "Character group".
- Character_group sameAs Q2720844.
- Character_group sameAs Carxc3xa0cter_dun_grup_finit.
- Character_group sameAs Caractxc3xa8re_dun_groupe_fini.
- Character_group sameAs 指標群.
- Character_group sameAs Caráter_de_um_grupo.
- Character_group sameAs m.04y9g9.
- Character_group sameAs Q2720844.
- Character_group wasDerivedFrom Character_group?oldid=681674528.
- Character_group isPrimaryTopicOf Character_group.