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Rational realization of the minimum ranks of nonnegative sign pattern matrices

Wei FangWei GaoYubin GaoFei GongGuangming JingZhongshan LiYan Ling ShaoLihua Zhang — 2016

Czechoslovak Mathematical Journal

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 2 and point-hyperplane configurations in r - 1 and Steinitz’s theorem on the rational realizability of...

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