Krylov subspace (source code)

= Krylov subspace
{c}
{title2=$\mathcal K_k(A,b)$}
{wiki}

The order-$k$ Krylov subspace generated by $A$ and $b$ is
$$
\mathcal K_k(A,b)=\operatorname{span}\{b,Ab,\ldots,A^{k-1}b\}.
$$