In order to figure out what range the eigenvalues of a certain matrix would be in we can use Gershgorin’s. Theorem. 1 Strictly Diagonally Dominant Matrices. ordering rows and columns PMP−1, where P is a permutation matrix.) Gershgorin Circle Theorem. Also called the Gershgorin Disk Theorem. Theorem statement. Gerschgorin theorem, Geršgorin theorem. Given a complex -matrix,, with, then finding the eigenvalues of is equivalent to finding the zeros of.
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The Gershgorin circle theorem where “Gershgorin” is sometimes also spelled “Gersgorin” or “Gerschgorin” identifies a region in the complex plane that contains all the eigenvalues of a complex square matrix. For an matrixdefine.
Then each eigenvalue of is in at least one of gfrschgorin disks. The theorem can be made stronger as follows. Let be an integer withand let be the sum of the magnitudes of the largest off-diagonal elements in column.

Then each eigenvalue of is either in one of the disks. Monthly 72, Monthly, Nauk 7, Tables of Integrals, Series, and Products, 6th ed. Monthly 56, Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.
Gershgorin circle theorem – Wikipedia
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Collection of teaching and learning tools built by Wolfram education experts: Mon Dec 31 Gershgorin Circles Chris Maes. Contact the MathWorld Team.
