Brualdi, Richard A. and Kirkland, Steve (2010) Totally Nonnegative (0, 1)Matrices. Linear Algebra and its Applications , 432 (7). pp. 16501662. ISSN 00243795
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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. 
Subjects:  Science & Engineering > Hamilton Institute Science & Engineering > Mathematics 
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 
URI: 
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