Definition
Affine Hyperplane
An affine hyperplane
is an affine subspace of dimension . It is a translate of a linear subspace of that dimension: The point
fixes the position of , and contains its directions. Equivalently, for a non-zero normal vector and an offset , Here
is the inner product. If , passes through the origin and is a linear subspace; if , it does not. The term hyperplane commonly includes both cases.