Linear Algebra, Plane

Hyperplane

Introduced by Soham in relation to K-d Tree.

In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. It’s essentially extending the definition of a plane to higher dimensionality.

In ${\mathbb{R}}^d$, a hyperplane can be written as $\pi :w^{T}x+b=0$ where

• $w\in {\mathbb{R}}^d$
• $x\in {\mathbb{R}}^d$
• $b$ is an offset