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Brualdi, Richard A. and Kirkland, Steve (2010) Totally Nonnegative (0, 1)-Matrices. Linear Algebra and its Applications , 432 (7). pp. 1650-1662. ISSN 0024-3795
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Abstract
We investigate (0, 1)-matrices which are totally nonnegative and therefore which have all of their eigenvalues equal to nonnegative real numbers. Such matrices are characterized by four forbidden submatrices (of orders 2 and 3). We show that the maximum number of 0s in an irreducible (0, 1)-matrix of order n is (n − 1)2 and
characterize those matrices with this number of 0s. We also show that the minimum Perron value of an irreducible, totally nonnegative (0, 1)-matrix of order n equals 2 + 2 cos (2∏/n+2) and characterize those matrices with this Perron value.
| Item Type: | Article |
|---|---|
| Keywords: | Totally nonnegative matrices; Digraphs; Spectrum; Eigenvalues (0, 1)-Matrices; Hamilton Institute. |
| Academic Unit: | Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics |
| Item ID: | 1893 |
| Identification Number: | 10.1016/j.laa.2009.11.021 |
| Depositing User: | Hamilton Editor |
| Date Deposited: | 22 Mar 2010 16:37 |
| Journal or Publication Title: | Linear Algebra and its Applications |
| Publisher: | Elsevier |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1893 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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