Wolfram Language

Gerschgorin Disks

The Gerschgorin circle theorem (http://mathworld.wolfram.com/GershgorinCircleTheorem.html) states that every eigenvalue of the square matrix is in at least one of the disks whose centers are the diagonal entries of and whose radii are a sum of the entries in each row.

Generate a random complex matrix .

The diagonal entries of are the centers of the Gerschgorin disks.

The radius of the th Gerschgorin disk, , is the sum of the moduli of the entries in row , excluding the diagonal entry.

Make the Gerschgorin disks for the matrix.

Show the eigenvalues (red) in the Gerschgorin disks.

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