Real Linear Functionals
Definition
A function $f: \R ^n \to \R $ is called a functional. If $f$ is linear, then $f(x) = a^\top x$ for all $x$. So every vector $a \in \R ^n$ can be thought to correspond to a linear functional.
A function $f: \R ^n \to \R $ is called a functional. If $f$ is linear, then $f(x) = a^\top x$ for all $x$. So every vector $a \in \R ^n$ can be thought to correspond to a linear functional.