Gershgorin Circles and Diagonally Dominant Matrices

We prove the Gershgorin Circle Theorem. Given an nxn matrix A withe real entries, we consider discs in the complex plane whose centers are the diagonal entries, a_{jj}, and whose radii are the sum of the absolute value of the other non-diagonal entries in the same row as a_{jj}. We show that every eigenvalue of the matrix must reside in at least one of these discs.

#mikethemathematician, #mikedabkowski, #profdabkowski

[godfreypigott]

Surely your title should say "dominant", not "dominate".