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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. Does every disk have its own eigenvalue? NO but. Theorem. Let A = [aij ] be an n × n complex matrix. If Di1,Di2,,Dik are Gershgorin discs of A that are. Aug 9, The Gershgorin disc theorem is an elementary result that allows you to make very fast deductions about the locations of eigenvalues.

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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.

Theogem an matrixdefine. Then each eigenvalue of is in at least one of the disks. The theorem can be made stronger as follows.

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Gershgorin circle theorem

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.

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Gershgorin circle theorem – Wikipedia

Practice online or make a printable study sheet. Collection of teaching and learning tools built by Wolfram education experts: Mon Dec 31 Gershgorin Circles Chris Maes. Contact the MathWorld Team.