Affine-linear mapping/Affine isomorphism/Definition

Affine isomorphism

Let ${}K$ be a field, and let ${}E$ and ${}F$ denote affine spaces over the ${}K$-vector spaces ${}V$ and ${}W$. A bijective affine-linear mapping

$\psi \colon E\longrightarrow F$

is called an affine isomorphism.