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Essential sign change numbers of full sign pattern matrices

Xiaofeng Chen;  Wei Fang;  Wei Gao;  Yubin Gao;  Guangming Jing;  Zhongshan Li;  Yanling Shao;  Lihua Zhang — 2016

Special Matrices

A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced for full sign...

Rational realization of the minimum ranks of nonnegative sign pattern matrices

Wei Fang;  Wei Gao;  Yubin Gao;  Fei Gong;  Guangming Jing;  Zhongshan Li;  Yan Ling Shao;  Lihua 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 r - 1 and Steinitz’s theorem on the rational realizability of...

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