Characteristic function: Difference between revisions

Revision as of 16:32, 3 March 2010

Revision as of 18:03, 5 March 2010

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::<math>\chi_{A} (x) := \begin{cases} 0, & x \in A; \\ + \infty, & x \not \in A. \end{cases}</math>

* The [[characteristic state function]] in statistical mechanics.

* In probability theory, the [[characteristic function (probability theory)]] 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:

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:where '''E''' means expected value. This concept extends to multivariate distributions.

* The [[characteristic polynomial]] in linear algebra.

* The [[Euler characteristic]], a topological invariant.

* The [[cooperative game]] in game theory.

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