Gershgorin disc ($D_i=\{z:|z-M_{ii}|\le {\sum }_{j\ne i}|M_{ij}|\}$)

For row $i$ of a matrix, the Gershgorin disc has centre $M_{ii}$ and radius ${\sum }_{j\ne i}|M_{ij}|$. The Gershgorin disc theorem places every eigenvalue in the union of these discs. For a Hermitian matrix the real intervals cut out by the discs bound energies; an isolated disc contains exactly one eigenvalue.