Affine Subspace

linear-logic

Definition

Affine Subspace

Let $V$ be a vector space. An affine subspace $A\subseteq V$ is a subset of $V$ that looks like a linear subspace, but has been shifted away from the origin.

Formally, a set $A\subseteq {\mathbb{R}}^d$ is an affine subspace if there exists a Linear subspace $U\subseteq {\mathbb{R}}^d$ and a translation vector $x_0\in {\mathbb{R}}^d$ such that:

$$A=x_0+U=\{x_0+u\mid u\in U\}$$