operator

An operator is a term with multiple related meanings in mathematics, computer science, and everyday usage. Broadly, it can refer to a person who operates a machine or device, or to a symbol or function that denotes an operation to be performed on operands. In mathematics and computing, the emphasis is on the latter: an operator specifies a rule that combines one or more inputs to produce an output.

In mathematics, common operators include arithmetic ones such as addition, subtraction, multiplication, and division, as well as more abstract notions like the derivative or integral operators. Relational operators compare values (equal, not equal, less than, greater than), and logical operators combine boolean values (and, or, not). In programming languages, operators are tokens that apply to operands and can be unary or binary, infix or prefix. Language design determines what operators exist, their precedence, associativity, and how they interact with various data types. Many languages also support operator overloading, allowing a single symbol to denote different operations depending on the operand types.

In functional analysis and linear algebra, an operator often means a mapping between function or vector spaces. A linear operator L satisfies linearity: L(a f + b g) = a L(f) + b L(g). Examples include differential operators, integral operators, and shift operators. Operator theory studies such mappings, their spectra, and algebraic properties.

Outside theory, an operator can be a person who operates equipment, such as a machine, crane, forklift, or aircraft, typically requiring training and certification. In communications or broadcasting, an operator may refer to staff who handle tasks at a call center or on the air. See also operator precedence and operator overloading for related concepts.