An operator (not to be confused with operation) is a mapping from one vector space or module to another. Operators are of critical importance to both linear algebra and functional analysis. Important properties that various operators may exhibit include linearity, continuity, and boundedness.

Important special cases of an operator include:

• Functional, which maps a vector space to its underlying field. The space of functionals over a vector space exhibits duality to it, which has numerous applications. Important applications of functionals are the theories of generalized functions, which extends the classical notion of a function and derivative, and calculus of variations, which generalizes the notion of differential to functionals as they are. Both are of great importance to theoretical physics.
• Linear operator, which has a number of characteristics that ease its study. Important examples of linear operators are integral and derivative. In finite-dimensional spaces linear operators are often represented by matrices.

Noun

opèrātor m. (Cyrillic spelling опѐра̄тор)

1. (mathematics) operator

Declension declension of operator singular plural nominative operator operatori genitive operatora operatora dative operatoru operatorima accusative operator operatore vocative operatore operatori locative operatoru operatorima instrumental operatorom operatorima

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