# Gershgorin Circle Theorem, mathematical derivation of eigenvalue estimates

1. Mar 28, 2012

### onako

I intend to use the Gershgorin Circle Theorem for estimating the eigenvalues of a real symmetric (n x n) matrix. Unfortunately, I'm a bit confused with the examples one might find on the internet; What would be the mathematical
formula for deriving estimates on eigenvalues?

I understand that certain disks are formed, each centered at the diagonal entry, with the radius equal to the summation of absolute values of the associated off-diagonal row entries. Which steps to take from this point to get the estimates on the eigenvalues?