Definition:Tangent Space (Affine Geometry)

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.

Also see

 * Definition:Tangent Space