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 $V = \vec{\mathcal E}$.

$V$ is also called the underlying vector space, or the translation space of the affine space $\mathcal E$; or the tangent space to $\mathcal E$.