Affine-linear mapping/Affine isomorphism/Definition

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

${\displaystyle \psi \colon E\longrightarrow F}$

is called an affine isomorphism.