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Totally Nonnegative (0, 1)-Matrices

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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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

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