Operator (mathematics)

In mathematics, an operator is a symbol or function that represents an action performed on one or more values to produce a new value. Operators are the verbs of mathematical expressions, transforming their inputs through defined rules.

The concept spans algebraic manipulation, calculus, and abstract structures. A simple example is addition (+), which combines two numbers. More sophisticated operators include differentiation (which transforms a function into its rate of change) and integration. In Linear algebra, operators like matrix multiplication act on vectors and spaces.

Operators form the foundation of functional thinking: they're reusable, composable units of work. In Quantum mechanics, operators represent observables—measurable physical quantities. The composition of operators (applying one after another) creates new operators, enabling elegant problem-solving across physics, Computer science, and Engineering.

Understanding operators unlocks deeper mathematical fluency. They clarify why certain equations behave as they do and why seemingly different problems share hidden structure.

Related

Function (mathematics), Linear algebra, Calculus, Quantum mechanics, Symbol (mathematics)