# Definition:Tangent Space (Affine Geometry)

This page is about tangent space in the context of affine spaces. For other uses, see Definition:Tangent Space.

## Definition

Let $\tuple {\mathcal E, +, -}$ be an affine space.

Let $V$ be the vector space that is the codomain of $-$.

Then $V$ is the tangent space of $\mathcal E$.

## Notation

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

## Also known as

The tangent space is also apparently known as the difference space.