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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 Hurwitz determinant ： ウィキペディア英語版 Hurwitz determinant In mathematics, Hurwitz determinants were introduced by , who used them to give a criterion for all roots of a polynomial to have negative real part. ==Definition== Let us consider a characteristic polynomial ''P'' in the variable ''λ'' of the form: :$$ P(\lambda)= a_0 \lambda^n + a_1 \lambda^ + \cdots + a_ \lambda + a_n where $a\_i$, $i=0,1,\backslash ldots,n$, are real. The square Hurwitz matrix associated to ''P'' is given below: :$$ H= \begin a_1 & a_3 & a_5 & \dots & \dots & \dots & 0 & 0 & 0 \\ a_0 & a_2 & a_4 & & & & \vdots & \vdots & \vdots \\ 0 & a_1 & a_3 & & & & \vdots & \vdots & \vdots \\ \vdots & a_0 & a_2 & \ddots & & & 0 & \vdots & \vdots \\ \vdots & 0 & a_1 & & \ddots & & a_n & \vdots & \vdots \\ \vdots & \vdots & a_0 & & & \ddots & a_ & 0 & \vdots \\ \vdots & \vdots & 0 & & & & a_ & a_n & \vdots \\ \vdots & \vdots & \vdots & & & & a_ & a_ & 0 \\ 0 & 0 & 0 & \dots & \dots & \dots & a_ & a_ & a_n \end. The ''i''th ''Hurwitz determinant'' is the determinant of the ''i''th leading principal minor of the above Hurwitz matrix ''H''. There are ''n'' Hurwitz determinants for a characteristic polynomial of degree ''n''. 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「Hurwitz determinant」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.