characteristic function (redirected from characteristic functions)

characteristic function [‚kar·ik·tə′ris·tik ′fəŋk·shən]

(mathematics)

The function χ_Adefined for any subsetAof a set by setting χ_A(x) = 1 ifxis inAand χ_A= 0 ifxis not inA. Also known as indicator function.

eigenfunction

(physics)

A function, such as the point characteristic function or the principal function, which is the integral of some property of an optical or mechanical system over time or over the path followed by the system, and whose value for a path actually followed by a system is a maximum or a minimum with respect to nearby paths with the same end points.

(statistics)

A function that uniquely defines a probability distribution; it is equal to √(2π) times the Fourier transform of the frequency function of the distribution.

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(mathematics)

characteristic function - The characteristic function of set returns True if its argument is an element of the set and False otherwise.