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:	https://doi.org/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
URI:	Publisher
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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