From Boolean to sign pattern matrices Original Research Article

A nonnegative sign pattern matrix is a matrix whose entries are from the set {+, 0}. A nonnegative sign pattern matrix can also be viewed as a Boolean matrix, by replacing each + entry with 1. In this paper, some interesting connections between nonnegative sign pattern matrices and Boolean matrices are investigated. In particular, the relations between the minimum rank and the Boolean row (or column) rank are explored; the idempotent Boolean matrices that allow idempotence are identified; and the nonnegative sign patterns that allow various types of nonnegative (or positive) generalized inverses are characterized.