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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 matrix ： ウィキペディア英語版 Hurwitz matrix In mathematics, a Hurwitz matrix, or Routh-Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients of a real polynomial. ==Hurwitz matrix and the Hurwitz stability criterion== Namely, given a real polynomial :$p(z)=a\_z^n+a\_z^+\backslash cdots+a\_z+a\_n$ the $n\backslash times\; n$ square matrix :$$ H= \begin a_1 & a_3 & a_5 & \dots & \dots & \dots & 0 & 0 & 0 \\ a_0 & a_2 & a_4 & & & & \vdots & \vdots & \vdots \\ 0 & a_1 & a_3 & & & & \vdots & \vdots & \vdots \\ \vdots & a_0 & a_2 & \ddots & & & 0 & \vdots & \vdots \\ \vdots & 0 & a_1 & & \ddots & & a_n & \vdots & \vdots \\ \vdots & \vdots & a_0 & & & \ddots & a_ & 0 & \vdots \\ \vdots & \vdots & 0 & & & & a_ & a_n & \vdots \\ \vdots & \vdots & \vdots & & & & a_ & a_ & 0 \\ 0 & 0 & 0 & \dots & \dots & \dots & a_ & a_ & a_n \end. is called Hurwitz matrix corresponding to the polynomial $p$. It was established by Adolf Hurwitz in 1895 that a real polynomial is stable (that is, all its roots have strictly negative real part) if and only if all the leading principal minors of the matrix $H(p)$ are positive: :$$ \begin \Delta_1(p) &= \begin a_ \end &&=a_ > 0 \\() \Delta_2(p) &= \begin a_ & a_ \\ a_ & a_ \\ \end &&= a_2 a_1 - a_0 a_3 > 0\\() \Delta_3(p) &= \begin a_ & a_ & a_ \\ a_ & a_ & a_ \\ 0 & a_ & a_ \\ \end &&= a_3 \Delta_2 - a_1 (a_1 a_4 - a_0 a_5 ) > 0 \end and so on. The minors $\backslash Delta\_k(p)$ are called the Hurwitz determinants. 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 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.