A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set $\{+,-,0\}$ ($\{+,0\}$, respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix $𝒜$ is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of $𝒜$. Using a correspondence between sign patterns with minimum rank $r\ge 2$ and point-hyperplane configurations in ${ℝ}^{r-1}$ and Steinitz’s theorem on the rational realizability of...