= Dominant eigenpair extraction from a two-step Krylov recurrence
{title2=$y_{k+2}=s y_{k+1}-p y_k$}
When two independent iterates span an invariant two-dimensional subspace, their recurrence gives the characteristic polynomial $\lambda^2-s\lambda+p$. For distinct roots $\lambda_1,\lambda_2$, corresponding eigenvectors are $y_{k+1}-\lambda_2y_k$ and $y_{k+1}-\lambda_1y_k$. For a merely approximately dominant subspace, the same computation gives approximate eigenpairs. A single orbit cannot separate a repeated eigenvalue's entire eigenspace when its projection is only one direction.
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