Definition:Affine Space/Difference Space

Definition
Let $\mathcal E$ be an affine space with associated operations $+$ and $-$.

The vector space $V$ that is the codomain of $-$ is called the difference space of $\mathcal E$.

It is common to write $V = \vec{\mathcal E}$.

Also known as
$V$ is also referred to as:
 * the underlying vector space of $\mathcal E$
 * the translation space of $\mathcal E$
 * the tangent space to $\mathcal E$.