Error Bound for Computed Eigenvectors.

Keeping the assignments to $\wtd\lambda$, $\lambda$, and $\delta$ as above, and letting $x$ be the eigenvector of $A$ corresponding to $\lambda$, we have the following error bound of the computed eigenvector $\wtd x$ [101,425]:

$$\sin\theta(x,\wtd x)\le\frac {\Vert r\Vert _2}{\delta}.$$ (65)