In mathematics, characteristic function can refer to any of several distinct concepts:
- The most common and universal usage is as a synonym for indicator function, that is the function
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- which for a given subset A of X, has value 1 at points of A and 0 at points of X − A.
- In probability theory, the characteristic function of any probability distribution on the real line is given by the following formula, where X is any random variable with the distribution in question:
- where E means expected value. This concept extends to multivariate distributions.
- The characteristic function in convex analysis:
- The characteristic state function in statistical mechanics.
- The characteristic polynomial in linear algebra.
- The Euler characteristic, a topological invariant.
- The cooperative game in game theory.
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