Definition:Tangent Map/Affine Transformation

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

Let $\LL: \EE \to \FF$ be an affine transformation.

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

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