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 see

 * Definition:Tangent Space