Gershgorin disks for multiple eigenvalues of non-negative matrices
Combinatorics
2016-09-26 v1 Spectral Theory
Abstract
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.
Cite
@article{arxiv.1609.07439,
title = {Gershgorin disks for multiple eigenvalues of non-negative matrices},
author = {Imre Bárány and József Solymosi},
journal= {arXiv preprint arXiv:1609.07439},
year = {2016}
}