Hyperplane

A hyperplane is a concept from geometry and linear algebra that refers to a subspace of one dimension less than its ambient space. In simple terms, if you have an \( n \)-dimensional space, a hyperplane would be an \( (n-1) \)-dimensional subspace. Here are some examples to clarify: 1. **In 2D (two-dimensional space)**: A hyperplane is a line. It divides the plane into two halves.

Generalization of a plane for any number of dimensions.

Kind of the opposite of a line: the line has dimension 1, and the plane has dimension D-1.

In $D=2$, both happen to coincide, a boring example of an exceptional isomorphism.