Operatorë

Operatorë is the Albanian plural form of operator, a term used across several disciplines to describe a rule or person that acts on inputs to produce outputs. In everyday language, operatorë can refer to people who operate machines or equipment, such as a factory operator or a crane operator. In mathematics, computer science, and physics, the concept has a more formal meaning: an operator is a rule that assigns to each element of one set another element, often in a way that preserves some structure.

In mathematics, operators are mappings between spaces. Linear operators satisfy T(ax + by) = aT(x) + bT(y) for vectors x and y and scalars a and b. Differential operators, such as the derivative D, act on functions to produce new functions (D(f) = f'). Integral operators map a function to another function via integration, while projection and rotation operators act within vector spaces. Operator theory studies properties of these mappings, including boundedness, spectra, adjoints, and continuity.

In computer science, operators include arithmetic (+, −, ×, ÷), logical (and, or, not), relational (equal, less than), and bitwise operators, among others. They appear in expressions to combine values and control flow, with rules for precedence and associativity that vary by language. Operator overloading and higher-order operators are common concepts in modern programming languages.

In physics and engineering, operators are used to describe observables and transformations, such as momentum or energy operators in quantum mechanics, where they act on state vectors to yield measurable quantities or evolved states.

See also: operator theory, operator (mathematics), operator (computer science).