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An operator is a mapping from one vector space or module to another. Operators are of critical importance to both linear algebra and functional analysis, and they find application in many other fields of pure and applied mathematics. For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by hermitian operators. Important properties that various operators may exhibit include linearity, continuity, and boundedness. == Definitions == Let ''U, V'' be two vector spaces. Any mapping from ''U'' to ''V'' is called an operator. Let ''V'' be a vector space over the field ''K''. We can define the structure of a vector space on the set of all operators from ''U'' to ''V'' (''A'' and ''B'' are operators): : : for all ''A, B: U → V'', for all x in ''U'' and for all ''α'' in ''K''. Additionally, operators from any vector space to itself form a unital associative algebra: : with the identity mapping (usually denoted ''E'', ''I'' or id) being the unit. 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「Operator (mathematics)」の詳細全文を読む スポンサード リンク
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