Linear part of an affine map
= Linear part of an affine map
{title2=$x\mapsto Ax+b$}
The map $A$ associated with an <affine map> $x\mapsto Ax+b$; it is independent of the translation $b$. An affine <Euclidean isometry> has an orthogonal linear part, and an <isometry> between <flat tori> has a lift whose linear part carries one <Euclidean lattice> onto the other.