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.
CITATION STYLE
Bárány, I., & Solymosi, J. (2017). Gershgorin disks for multiple eigenvalues of non-negative matrices. In A Journey through Discrete Mathematics: A Tribute to Jiri Matousek (pp. 123–133). Springer International Publishing. https://doi.org/10.1007/978-3-319-44479-6_6
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