Rational realization of the minimum ranks of nonnegative sign pattern matrices
A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set (, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of . Using a correspondence between sign patterns with minimum rank and point-hyperplane configurations in and Steinitz’s theorem on the rational realizability of...