Gershgorin Circles

sample matrix

1

random matrix

random seed

size of random matrix

3

4

5

6

7

8

off-diagonal weight

row	column

row ⋂ column

Gershgorin's circle theorem states that the eigenvalues of a matrix are contained within a union of a series of disks in the complex plane. The centers of these disks are given by the diagonal elements of the matrix; the radii by sum of the absolute values of the off-diagonal elements in the corresponding row or column. Eigenvalues are shown in red.

External Links

Gershgorin Circle Theorem (Wolfram MathWorld)

Eigenvalue (Wolfram MathWorld)

Permanent Citation

Chris Maes

"Gershgorin Circles"
http://demonstrations.wolfram.com/GershgorinCircles/
Wolfram Demonstrations Project
Published: April 27, 2007