Hyperplane

linear-algebra

Definition

Hyperplane

A hyperplane is an affine subspace of dimension $d-1$ in a $d$-dimensional vector space ${\mathbb{R}}^d$.

It’s defined by a normal vector $w\in {\mathbb{R}}^d$ and a bias term $b\in \mathbb{R}$. The set of points $x$ that form the hyperplane satisfies the linear equation:

$$H=\{x\in {\mathbb{R}}^d\mid ⟨w,x⟩+b=0\}$$

where $$