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Gershgorin circle theorem [wikipedia] - mklabgr - 06-18-2026
Summary
The Gershgorin Circle Theorem is a result in linear algebra that provides a way to estimate the locations of the eigenvalues of a square matrix without calculating them directly. It states that every eigenvalue of a matrix lies within at least one of the Gershgorin discs, which are circular regions in the complex plane centered at each diagonal entry of the matrix, with radius equal to the sum of the absolute values of the other entries in the same row (or column).
The theorem is useful for understanding matrix stability, approximating eigenvalue distributions, and simplifying problems in numerical analysis. It was introduced by the Russian mathematician Semyon Gershgorin in 1931 and remains an important tool in computational mathematics and spectral theory.
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