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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 Inverse relation ： ウィキペディア英語版 Inverse relation In mathematics, the inverse relation of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the inverse of the relation 'child of' is the relation 'parent of'. In formal terms, if $X\; \backslash text\; Y$ are sets and $L\; \backslash subseteq\; X\; \backslash times\; Y$ is a relation from ''X'' to ''Y'' then $L^$ is the relation defined so that $y\backslash ,L^\backslash ,x$ if and only if $x\backslash ,L\backslash ,y$. In set-builder notation, $L^\; =\; \backslash$. The notation comes by analogy with that for an inverse function. Although many functions do not have an inverse; every relation does have a unique inverse. Despite the notation and terminology, the inverse relation is ''not'' an inverse in the sense of group inverse; the unary operation that maps a relation to the inverse relation is however an involution, so it induces the structure of a semigroup with involution on the binary relations on a set, or more generally induces a dagger category on the category of relations as detailed below. As a unary operation, taking the inverse (sometimes called inversion) commutes however with the order-related operations of relation algebra, i.e. it commutes with union, intersection, complement etc. The inverse relation is also called the converse relation or transpose relation— the latter in view of its similarity with the transpose of a matrix. It has also been called the opposite or dual of the original relation. Other notations for the inverse relation include or $\backslash breve$ or or . ==Examples== For usual (maybe strict or partial) order relations, the converse is the naively expected "opposite" order, e.g. , etc. 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「Inverse relation」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.