Could someone please help me show that if A is Hermitian(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\left\|(A-\lambda I)^{-1}\right\|_{2}=\frac{1}{min_{\lambda_{i}\in\sigma(A)}|\lambda-\lambda_{i}|}[/tex]

where [tex]\sigma(A)[/tex] denotes the eigenvalues of A.

I have figured out how to solve the norm without an inverse, but the inverse confuses me a bit.

Recall, that [tex]\left\|\cdot\right\|=\sqrt{r_{\sigma}(A^{*}A)}[/tex], which is to say the square root of the largest eigenvalue of [tex]A^{*}A[/tex].

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Matrix Norms

**Physics Forums | Science Articles, Homework Help, Discussion**