Gershgorin Circle Theorem
Visualize eigenvalue localization discs and diagonal dominance on the complex plane.
Free theory articleVisualize eigenvalue localization discs and diagonal dominance on the complex plane.
Concept & interpretation
Computing the exact eigenvalues of an n × n matrix requires finding roots of an n-th degree characteristic polynomial, which has no closed-form formula for n ≥ 5 by the Abel-Ruffini theorem. The Gershgorin Circle Theorem, published by Soviet mathematician Semyon Aranovich Gershgorin in 1931, provides geometric circular bounds on the complex plane directly from row and column sums of the matrix entries, requiring zero polynomial factorizations.