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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 Biorthogonal system ： ウィキペディア英語版 Biorthogonal system In mathematics, a biorthogonal system is a pair of indexed families of vectors :$\backslash tilde\; v\_i$ in and $\backslash tilde\; u\_i$ in such that :$\backslash langle\backslash tilde\; v\_i\; ,\; \backslash tilde\; u\_j\backslash rangle\; =\; \backslash delta\_\; ,$ where ''E'' and ''F'' form a pair of topological vector spaces that are in duality, is a bilinear mapping and $\backslash delta\_$ is the Kronecker delta. A biorthogonal system in which and $\backslash tilde\; v\_i\; =\; \backslash tilde\; u\_i$ is an orthonormal system. An example is the pair of sets of respectively left and right eigenvectors of a matrix, indexed by eigenvalue. ==Projection== Related to a biorthogonal system is the projection :$P:=\; \backslash sum\_\; \backslash tilde\; u\_i\; \backslash otimes\; \backslash tilde\; v\_i$, where $\backslash left(\; u\; \backslash otimes\; v\backslash right)\; (x):=\; u\; \backslash langle\; v,\; x\backslash rangle$; its image is the linear span of $\backslash$, and the kernel is $\backslash$. 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「Biorthogonal system」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.