Interactive Educational Modules in
Scientific Computing

Gershgorin's Theorem

This module demonstrates localization of eigenvalues in the complex plane using Gershgorin's Theorem. According to Gershgorin's Theorem, the eigenvalues of a matrix are contained within the union of disks, with each disk centered at a diagonal entry of the matrix and having radius equal to the sum of absolute values of off-diagonal entries in that row.

The user first selects a matrix size, then selects a matrix by choosing a preset example, a random matrix, or typing in desired entries. The eigenvalues of the matrix are then shown as red dots in the complex plane, and the corresponding Gershgorin circles are drawn in blue.

Reference: Michael T. Heath, Scientific Computing, An Introductory Survey, 2nd edition, McGraw-Hill, New York, 2002. See Section 4.2.5, especially Example 4.6 and Figure 4.2.

Developers: Jeffrey Naisbitt and Michael Heath