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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 Alternant matrix ： ウィキペディア英語版 Alternant matrix In linear algebra, an alternant matrix is a matrix with a particular structure, in which successive columns have a particular function applied to their entries. An alternant determinant is the determinant of an alternant matrix. Such a matrix of size ''m'' × ''n'' may be written out as :$M=\backslash begin$ f_1(\alpha_1) & f_2(\alpha_1) & \dots & f_n(\alpha_1)\\ f_1(\alpha_2) & f_2(\alpha_2) & \dots & f_n(\alpha_2)\\ f_1(\alpha_3) & f_2(\alpha_3) & \dots & f_n(\alpha_3)\\ \vdots & \vdots & \ddots &\vdots \\ f_1(\alpha_m) & f_2(\alpha_m) & \dots & f_n(\alpha_m)\\ \end or more succinctly :$M\_\; =\; f\_j(\backslash alpha\_i)$ for all indices ''i'' and ''j''. (Some authors use the transpose of the above matrix.) Examples of alternant matrices include Vandermonde matrices, for which $f\_i(\backslash alpha)=\backslash alpha^$, and Moore matrices, for which $f\_i(\backslash alpha)=\backslash alpha^$ 1 & \alpha_1 & \dots & \alpha_1^ \\ 1 & \alpha_2 & \dots & \alpha_2^ \\ 1 & \alpha_3 & \dots & \alpha_3^ \\ \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_n & \dots & \alpha_n^ \\ \end (a Vandermonde matrix), then $\backslash prod\_\; (\backslash alpha\_j\; -\; \backslash alpha\_i)\; =\; \backslash det\; V$ divides such polynomial alternant determinants. The ratio $\backslash frac$ is called a bialternant. The case where each function $f\_j(x)\; =\; x^$ forms the classical definition of the Schur polynomials. Alternant matrices are used in coding theory in the construction of alternant codes. ==See also== * 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「Alternant 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.