Definition:Tangent Map/Affine Transformation

Definition
Let $\mathcal E$ and $\mathcal F$ be affine spaces with difference spaces $E$ and $F$ respectively.

Let $\mathcal L : \mathcal E \to \mathcal F$ be an affine transformation.

The associated linear transformation $L: E \to F$ of difference spaces is called the tangent map of $\mathcal L$.

Also known as
The tangent map of $\mathcal L$ is also known as the linear part of $\mathcal L$.