Operator

:This article is about operators in mathematics, for other kinds of operators see operator (disambiguation).

Related Topics:
Mathematics - Operator (disambiguation)

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In mathematics, an operator is some kind of function; if it comes with a specified type of operand as function domain, it is no more than another way of talking of functions of a given type. The most frequently met usage is a mapping between vector spaces; this kind of operator is distinguished by taking one vector and returning another. For example, consider an enlargement, say by a factor of √2; such as is required to take one size of DIN paper to another. It can also be applied geometrically to vectors as operands.

Related Topics:
Mathematics - Function - Operand - Function domain - Vector space - Enlargement - DIN

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In many important cases, operators transform functions into other functions. We also say an operator maps a function to another. The operator itself is a function, but has an attached type indicating the correct operand, and the kind of function returned. This extra data can be defined formally, using type theory; but in everyday usage saying operator flags its significance. Functions can therefore conversely be considered operators, for which we forget some of the type baggage, leaving just labels for the domain and codomain.

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