ABSTRACT
Definition. A functional is an application defined on a linear space X, or on a part of X, with values in the field of scalars on which the linear space X is defined. (N.B. The French term for a field is corps; in English, a field is a corps commutatif). In other words, a functional can be considered as a ”function” whose domain consists of a set of functions, and whose codomain is a set of scalars (numbers, figures, etc.). This definition shows that, in fact, a functional is an operator.
