Definition:Hyperplane/Definition 3

Definition

Let $X$ be a vector space.

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

$U$ is a hyperplane (in $X$) if and only if:

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

• Results about hyperplanes can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hyperplane