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In mathematics, the term "'''characteristic function'''" can refer to any of several distinct concepts:
* As a synonym for the [[indicator function]], that is the function
::<math>\mathbf{1}_A\colon X \to \{0, 1\},</math>
:which for a given subset ''A'' of ''X'', has value 1 at points of ''A'' and 0 at points of ''X'' − ''A''.
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* The [[characteristic function (convex analysis) | characteristic function]] in convex analysis:
::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>
* The characteristic function of a [[cooperative game]] in game theory.
* The [[characteristic polynomial]] in linear algebra.
* The [[characteristic state function]] in statistical mechanics.
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