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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 Wronskian ： ウィキペディア英語版 Wronskian In mathematics, the Wronskian (or Wrońskian) is a determinant introduced by and named by . It is used in the study of differential equations, where it can sometimes show linear independence in a set of solutions. ==Definition== The Wronskian of two differentiable functions and is . More generally, for real- or complex-valued functions , which are times differentiable on an interval , the Wronskian as a function on is defined by :$$ W(f_1, \ldots, f_n) (x)= \begin f_1(x) & f_2(x) & \cdots & f_n(x) \\ f_1'(x) & f_2'(x) & \cdots & f_n' (x)\\ \vdots & \vdots & \ddots & \vdots \\ f_1^(x)& f_2^(x) & \cdots & f_n^(x) \end,\qquad x\in I. That is, it is the determinant of the matrix constructed by placing the functions in the first row, the first derivative of each function in the second row, and so on through the th derivative, thus forming a square matrix sometimes called a fundamental matrix. When the functions are solutions of a linear differential equation, the Wronskian can be found explicitly using Abel's identity, even if the functions are not known explicitly. 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「Wronskian」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.