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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 Koecher–Vinberg theorem ： ウィキペディア英語版 Koecher–Vinberg theorem In operator algebra, the Koecher–Vinberg theorem is a reconstruction theorem for real Jordan algebras. It was proved independently by Max Koecher in 1957 and Ernest Vinberg in 1961. It provides a one-to-one correspondence between formally real Jordan algebras and so-called domains of positivity. Thus it links operator algebraic and convex order theoretic views on state spaces of physical systems. ==Statement== A convex cone $C$ is called ''regular'' if $a=0$ whenever both $a$ and $-a$ are in the closure $\backslash overline$. A convex cone $C$ in a vector space $A$ with an inner product has a ''dual cone'' $C^$ * = \. The cone is called ''self-dual'' when $C=C^$ *. It is called ''homogeneous'' when to any two points $a,b\; \backslash in\; C$ there is a real linear transformation $T\; \backslash colon\; A\; \backslash to\; A$ that restricts to a bijection $C\; \backslash to\; C$ and satisfies $T(a)=b$. The Koecher–Vinberg theorem now states that these properties precisely characterize the positive cones of Jordan algebras. Theorem: There is a one-to-one correspondence between formally real Jordan algebras and convex cones that are: * open; * regular; * homogeneous; * self-dual. Convex cones satisfying these four properties are called ''domains of positivity'' or ''symmetric cones''. The domain of positivity associated with a real Jordan algebra $A$ is the interior of the 'positive' cone $A\_+\; =\; \backslash$. 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「Koecher–Vinberg theorem」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.