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.
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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