Affine iteration
= Affine iteration
{title2=$x_{k+1}=Mx_k+c$}
Iterating an <affine map> gives $x_k=M^{k-1}x_1+\sum_{j=0}^{k-2}M^jc$. A <fixed point> exists exactly when $c$ is in the <image of a linear map> $I-M$. If the <spectral radius> of $M$ is below one, its <matrix powers> tend to zero and every orbit converges to the unique <fixed point> $(I-M)^{-1}c$.