In
mathematics, and particularly in
functional analysis and the
calculus of variations, a
functional is a
function from a
vector space into its underlying
scalar field, or a set of functions of the real numbers. In other words, it is a function that takes a vector as its input argument, and returns a
scalar. Commonly the vector space is a space of functions, thus the functional takes a function for its input argument, then it is sometimes considered a
function of a function. Its use originates in the
calculus of variations where one searches for a function that minimizes a certain functional. A particularly important application in
physics is searching for a state of a system that minimizes the
energy functional.