Definition:Hyperplane/Definition 3

Definition
Let $X$ be a vector space.

Let $U$ be a proper subspace of $X$.

$U$ is a hyperplane (in $X$) :


 * there exists a non-zero linear functional $\phi : X \to \Bbb F$ such that:
 * $U = \map \ker \phi$

Also see

 * Equivalence of Definitions of Hyperplane