# 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 $\mathcal E$.