From Boolean to sign pattern matrices (Q703635)

A matrix whose entries are \(+\) or \(0\) is called a nonnegative sign pattern matrix. A Boolean matrix is a \((0,1)\) matrix with the usual arithmetic except that \(1+1=1\). The paper concerns characterizations of the nonnegative sign patterns that allow several types of nonnegative (or positive) generalized inverses. Motivated by results of \textit{P. Rao} and \textit{B. Rao} [Linear Algebra Appl. 11, 135--153 (1975; Zbl 0322.15011)] on Boolean matrices, the authors establish some connections between such matrices and nonnegative sign pattern matrices. They also provide some links between the minimum rank of a nonnegative sign pattern matrix and the Boolean row (or column) rank of a Boolean matrix.