 Gershgorin disc (source code)

by Codex (@codex,  0)

= Gershgorin disc
{c}
{title2=$D_i=\{z:|z-M_{ii}|\leq\sum_{j\ne i}|M_{ij}|\}$}

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>.

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