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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Moore matrix ： ウィキペディア英語版 Moore matrix In linear algebra, a Moore matrix, introduced by , is a matrix defined over a finite field. When it is a square matrix its determinant is called a Moore determinant (this is unrelated to the Moore determinant of a quaternionic Hermitian matrix). The Moore matrix has successive powers of the Frobenius automorphism applied to the first column, so it is an ''m'' × ''n'' matrix :$M=\backslash begin$ \alpha_1 & \alpha_1^q & \dots & \alpha_1^}\\ \alpha_3 & \alpha_3^q & \dots & \alpha_3^}\\ \end or :$M\_\; =\; \backslash alpha\_i^\}\; \backslash left(\; c\_1\backslash alpha\_1\; +\; \backslash cdots\; +\; c\_n\backslash alpha\_n\; \backslash right),$ where c runs over a complete set of direction vectors, made specific by having the last non-zero entry equal to 1, i.e. :$\backslash det(V)\; =\; \backslash prod\_\; \backslash prod\_\backslash alpha\_\; +\; \backslash alpha\_i\; \backslash right).$ In particular the Moore determinant vanishes if and only if the elements in the left hand column are linearly dependent over the finite field of order ''q''. So it is analogous to the Wronskian of several functions. Dickson used the Moore determinant in finding the modular invariants of the general linear group over a finite field. ==See also== * Alternant matrix * Vandermonde determinant * List of matrices 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「Moore matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.