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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 Metzler matrix ： ウィキペディア英語版 Metzler matrix In mathematics, a Metzler matrix is a matrix in which all the off-diagonal components are nonnegative (equal to or greater than zero) : $\backslash qquad\; \backslash forall\_\backslash ,\; x\_\; \backslash geq\; 0.$ It is named after the American economist Lloyd Metzler. Metzler matrices appear in stability analysis of time delayed differential equations and positive linear dynamical systems. Their properties can be derived by applying the properties of nonnegative matrices to matrices of the form ''M'' + ''aI'' where ''M'' is a Metzler matrix. == Definition and terminology == In mathematics, especially linear algebra, a matrix is called Metzler, quasipositive (or quasi-positive) or essentially nonnegative if all of its elements are non-negative except for those on the main diagonal, which are unconstrained. That is, a Metzler matrix is any matrix ''A'' which satisfies :$A=(a\_);\backslash quad\; a\_\backslash geq\; 0,\; \backslash quad\; i\backslash neq\; j.$ Metzler matrices are also sometimes referred to as $Z^$-matrices, as a ''Z''-matrix is equivalent to a negated quasipositive matrix. * Nonnegative matrices * Positive matrix * Delay differential equation * M-matrix * P-matrix * Z-matrix * Stochastic matrix 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「Metzler 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.