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[Gershgorin’s famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper.]
Published: May 9, 2017
Keywords: Gershgorin Disks; Eigenvalue Multiplicity; Rearrangement Inequality; Hermitian Positive Semidefinite Matrix; Hesse Configuration
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