Every eigenvalue of a square matrix lies within at least one of a set of disks in the complex plane, each centered at a diagonal entry with radius equal to the sum of the absolute values of the other entries in that row. Named for Semyon Gershgorin, it gives a quick way to localize eigenvalues without computing them exactly.
Facts
StatementEvery eigenvalue of a complex square matrix A lies within at least one Gershgorin disc D(a_ii, R_i), the disc centered at diagonal entry a_ii with radius R_i equal to the sum of the absolute values of the other entries in row i. 1 Classification
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Source MacTutor History of Mathematics: Semyon Gershgorin
Sources
1. Gershgorin circle theorem (Wikipedia)
Wikimedia FoundationLead section, first sentence
In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix.
Lead section, second sentence
It was first published by the Soviet mathematician Semyon Aronovich Gershgorin in 1931.
In Group: Linear Algebra and Matrix Theory, Lead section
Theorem) may be used to bound the spectrum of a square matrix. It was first published by the Soviet mathematician
View the Source MacTutor History of Mathematics: Semyon Gershgorin
Proved By: Semyon Aranovich Gershgorin, Biography textQuote, Proved By: Semyon Aranovich Gershgorin, Biography text
In this paper he gave powerful estimates for matrix eigenvalues, known as his Circle Theorem.
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