Category:Definitions/Linear Functionals

This category contains definitions related to Linear Functionals.
Related results can be found in Category:Linear Functionals.

Let $E$ be a vector space over a field $\GF$.

Let $D$ be a linear subspace of $E$.

A mapping $f : D \to \GF$ is called a linear functional if and only if:

$\map f {\alpha x + \beta y} = \alpha \map f x + \beta \map f y$

holds for all $x, y$ in $L$ and for all $\alpha, \beta$ in $\GF$.