Gerschgorin Circle Theorem

Topic(s):

Illustrates how the Gershgorin circle theorem can be used to bound the eigenvalues of a matrix. You can select a random \(4\times4\) matrix or a special \(4\times4\) matrix that has at least one disjoint Gershgorin circle. You can see either the separate Gershgorin circles with the eigenvalues or a plot that superimposes all the circles.

Identifier:

http://demonstrations.wolfram.com/GershgorinCircleTheorem/

Subject:

Linear Algebra

Eigenvalues and Eigenvectors

Rating:

Creator(s):

Housam Binous and Brian G. Higgins

Cataloger:

David Poole

Publisher:

Wolfram Demonstrations Project

Rights:

Housam Binous, Brian G. Higgins and Wolfram Research

Format Other:

Requires down loading the CDF player from Wolfram (https://www.wolfram.com/cdf-player/).

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Comments

very effective at displaying the Gerschgorin circles

Permalink Submitted by Anonymous (not verified) on Tue, 2014-07-29 02:00

This applet is very effective at displaying the Gerschgorin circles associated with the eigenvalues of a \(4\times4\) matrix. User-defined matrices are not allowed but users can select either a random matrix or a pre-defined matrix that has a disjoint Gerschgorin circle. The actual eigenvalues and the radii of the circles are computed.