# Gershgorin Circle Theorem

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This Demonstration illustrates how the Gershgorin circle theorem can be used to bound the eigenvalues of an matrix . The theorem states that the eigenvalues of must lie in circles defined in the complex plane that are centered on the diagonal elements of with radii determined by the row-norms of , that is, and . If of the circles form a connected region disjoint from the remaining circles, then the region contains exactly eigenvalues.

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Contributed by: Housam Binous and Brian G. Higgins (April 2012)

Open content licensed under CC BY-NC-SA

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Reference

[1] B. Noble, *Applied Linear Algebra*, New Jersey: Prentice–Hall, 1969.

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