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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 Product numerical range ： ウィキペディア英語版 Product numerical range Given a Hilbert space with a tensor product structure a product numerical range is defined as a numerical range with respect to the subset of product vectors. In some situations, especially in the context of quantum mechanics product numerical range is known as local numerical range == Introduction == Let $X$ be an operator acting on an $N$-dimensional Hilbert space $\backslash mathcal\_N$. Let $\backslash mathrm(X)$ denote its ''numerical range'', ''i.e.'' the set of all $\backslash lambda$ such that there exists a normalized state $\backslash in$ \mathcal_N, $||\; \backslash psi\; ||\; =\; 1$, which satisfies $X\; =$ \lambda. An analogous notion can be defined for operators acting on a composite Hilbert space with a tensor product structure. Consider first a bi–partite Hilbert space, $\backslash mathcal\_N\; =\; \backslash mathcal\_K\; \backslash otimes\; \backslash mathcal\_M\; ,$ of a composite dimension $N=KM$. Let $X$ be an operator acting on the composite Hilbert space. We define the ''product numerical range'' $\backslash mathrm^\backslash !\; \backslash left(\; X\; \backslash right)$ of $X$, with respect to the tensor product structure of $\backslash mathcal\_N$, as $\backslash mathrm^\backslash !\; \backslash left(\; X\; \backslash right)\; =\; \backslash left\backslash$ : \in \mathcal_K, \in \mathcal_M \right\}, where $\backslash in\; \backslash mathcal\_K$ and $\backslash in\; \backslash mathcal\_M$ are normalized. 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「Product numerical range」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.