= Hyperplane separation theorem
{wiki}
= Separating hyperplane theorem
{synonym}
Two nonempty disjoint <convex sets> in a finite-dimensional real <vector space> admit a separating nonzero <linear functional>: for an appropriate $h\ne0$ and $a$, $h\cdot x\leq a\leq h\cdot y$ on the respective sets. Strict separation requires additional assumptions, such as one set being compact and the other closed. For an open <convex cone> $C$ excluding zero, separation from $\{0\}$ gives $h\cdot c\geq0$ for all $c\in C$; scaling cone elements forces the separating level to be zero. This finite-dimensional result is related to the <supporting hyperplane theorem>.
Back to article page
