Bárány, I;
Solymosi, J;
(2017)
Gershgorin Disks for Multiple Eigenvalues of Non-negative Matrices.
In: Loebl, M and Nešetřil, J and Thomas, R, (eds.)
A Journey Through Discrete Mathematics: A Tribute to Jiří Matoušek.
(pp. 123-133).
Springer: Cham, Switzerland.
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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.
| Type: | Book chapter |
|---|---|
| Title: | Gershgorin Disks for Multiple Eigenvalues of Non-negative Matrices |
| ISBN-13: | 9783319444789 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-319-44479-6_6 |
| Publisher version: | https://doi.org/10.1007/978-3-319-44479-6_6 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1518381 |
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