# Definition:Tangent Map/Affine Transformation

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## 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 $\mathcal L$.