Composition of affine transformations
= Composition of affine transformations
If $f(x)=Ax+b$ and $g(x)=Cx+d$, their <function composition> is $g(f(x))=CAx+Cb+d$, again an <affine map>. With column-vector <homogeneous coordinates>, its matrix is the product of the matrix for $g$ with that for $f$, so the rightmost factor acts first.