# Matrix Norms

1. Feb 27, 2010

### jschmid2

$$\left\|(A-\lambda I)^{-1}\right\|_{2}=\frac{1}{min_{\lambda_{i}\in\sigma(A)}|\lambda-\lambda_{i}|}$$
where $$\sigma(A)$$ denotes the eigenvalues of A.
Recall, that $$\left\|\cdot\right\|=\sqrt{r_{\sigma}(A^{*}A)}$$, which is to say the square root of the largest eigenvalue of $$A^{*}A$$.