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
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.
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