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
- which for every subset A of X, has value 1 at points of A and 0 at points of X − A.
- 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:
- where E means expected value. This concept extends to multivariate distributions.
- The characteristic function (convex analysis) 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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characteristic function — noun A function which is equal to 1 for all points in its domain which belong to a given set, and is equal to 0 for all points in the domain which do not belong to that given set. The characteristic function of a set A is often represented as… … Wiktionary
characteristic function — būdingoji funkcija statusas T sritis chemija apibrėžtis Būsenos funkcija, kurios diferencialinėmis išraiškomis galima nusakyti visas termodinaminės sistemos savybes. atitikmenys: angl. characteristic function rus. характеристическая функция … Chemijos terminų aiškinamasis žodynas
characteristic function — būdingoji funkcija statusas T sritis fizika atitikmenys: angl. characteristic function vok. charakteristische Funktion, f rus. характеристическая функция, f pranc. fonction caractéristique, f … Fizikos terminų žodynas
characteristic function — Math. 1. a function defined on a given set, having value 1 for every element of the set and value 0 for every element not contained in the set. 2. See characteristic polynomial. [1875 80] * * * … Universalium
characteristic function — noun : eigenfunction … Useful english dictionary
Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued … Wikipedia
Characteristic function (convex analysis) — In the field of mathematics known as convex analysis, the characteristic function of a set is a convex function that indicates the membership (or non membership) of a given element in that set. It is similar to the usual indicator function, and… … Wikipedia
Characteristic — (from the Greek word for a property or attribute (= trait) of an entity) may refer to: In physics and engineering, any characteristic curve that shows the relationship between certain input and output parameters, for example: I V or current… … Wikipedia
Characteristic polynomial — This article is about the characteristic polynomial of a matrix. For the characteristic polynomial of a matroid, see Matroid. For that of a graded poset, see Graded poset. In linear algebra, one associates a polynomial to every square matrix: its … Wikipedia
Characteristic state function — The characteristic state function in statistical mechanics refers to a particular relationship between the partition function of an ensemble. In particular, if the partition function P satisfies P = exp( − βQ) or P = exp( + βQ) in which Q is a… … Wikipedia