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- Brandt_matrix abstract "In mathematics, Brandt matrices are matrices, introduced by Brandt (1943), that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra.Eichler (1955) calculated the traces of the Brandt matrices.Let O be an order in a quaternion algebra with class number H, and Ii,...,IH left O-ideals representing the classes. Fix an integer m. Let ej denote the number of units in the right order of Ij and let Bij denote the number of α in Ij−1Ii with reduced norm N(α) equal to mN(Ii)/N(Ij). The Brandt matrix B(m) is the H×H matrix with entries Bij. Up to conjugation by a permutation matrix it is independent of the choice of representatives Ij; it is dependent only on the level of the order O.".
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- Brandt_matrix wikiPageWikiLink American_Mathematical_Society.
- Brandt_matrix wikiPageWikiLink Category:Matrices.
- Brandt_matrix wikiPageWikiLink Category:Number_theory.
- Brandt_matrix wikiPageWikiLink Central_simple_algebra.
- Brandt_matrix wikiPageWikiLink Class_number_(number_theory).
- Brandt_matrix wikiPageWikiLink Crelles_Journal.
- Brandt_matrix wikiPageWikiLink Hecke_algebra.
- Brandt_matrix wikiPageWikiLink Ideal_(ring_theory).
- Brandt_matrix wikiPageWikiLink Ideal_class_group.
- Brandt_matrix wikiPageWikiLink Journal_für_die_reine_und_angewandte_Mathematik.
- Brandt_matrix wikiPageWikiLink Matrix_(mathematics).
- Brandt_matrix wikiPageWikiLink Order_(ring_theory).
- Brandt_matrix wikiPageWikiLink Permutation_matrix.
- Brandt_matrix wikiPageWikiLink Quaternion_algebra.
- Brandt_matrix wikiPageWikiLink Rational_number.
- Brandt_matrix wikiPageWikiLink Reduced_norm.
- Brandt_matrix wikiPageWikiLink Springer-Verlag.
- Brandt_matrix wikiPageWikiLink Springer_Science+Business_Media.
- Brandt_matrix wikiPageWikiLinkText "Brandt matrix".
- Brandt_matrix hasPhotoCollection Brandt_matrix.
- Brandt_matrix wikiPageUsesTemplate Template:Citation.
- Brandt_matrix wikiPageUsesTemplate Template:Harvs.
- Brandt_matrix wikiPageUsesTemplate Template:Harvtxt.
- Brandt_matrix subject Category:Matrices.
- Brandt_matrix subject Category:Number_theory.
- Brandt_matrix hypernym Matrices.
- Brandt_matrix type Field.
- Brandt_matrix type Matrix.
- Brandt_matrix comment "In mathematics, Brandt matrices are matrices, introduced by Brandt (1943), that are related to the number of ideals of given norm in an ideal class of a definite quaternion algebra over the rationals, and that give a representation of the Hecke algebra.Eichler (1955) calculated the traces of the Brandt matrices.Let O be an order in a quaternion algebra with class number H, and Ii,...,IH left O-ideals representing the classes. Fix an integer m.".
- Brandt_matrix label "Brandt matrix".
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- Brandt_matrix sameAs Q4957187.
- Brandt_matrix sameAs Q4957187.
- Brandt_matrix wasDerivedFrom Brandt_matrix?oldid=621774499.
- Brandt_matrix isPrimaryTopicOf Brandt_matrix.