Category:Linear Functionals

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This category contains results about Linear Functionals.
Definitions specific to this category can be found in Definitions/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 $\GF$.