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In mathematics, Brandt matrices are matrices, introduced by , 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. calculated the traces of the Brandt matrices. Let ''O'' be an order in a quaternion algebra with class number ''H'', and ''I''i,...,''I''''H'' left ''O''-ideals representing the classes. Fix an integer ''m''. Let ''e''''j'' denote the number of units in the right order of ''I''''j'' and let ''B''''ij'' denote the number of α in ''I''''j''−1''I''''i'' with reduced norm N(α) equal to ''m''N(''I''''i'')/N(''I''''j''). The Brandt matrix ''B''(''m'') is the ''H''×''H'' matrix with entries ''B''''ij''. Up to conjugation by a permutation matrix it is independent of the choice of representatives ''I''''j''; it is dependent only on the level of the order ''O''. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brandt matrix」の詳細全文を読む スポンサード リンク
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