A sign pattern matrix is a matrix whose entries are from the set {+, -, 0}. If A is an m × n sign pattern matrix, the qualitative class of A, denoted Q(A), is the set of all real m×n matrices B = [b_(i,j) ] with b_(i,j) positive (respectively, negative, zero) if a_(i,j) is + (respectively, -, 0). The minimum rank of a sign pattern matrix A, denoted mr(A), is the minimum of the ranks of the real matrices in Q(A). Determination of the minimum rank of a sign pattern matrix is a longstanding open problem. For the case that the sign pattern matrix has a 1-separation, we present a formula to compute the minimum rank of a sign pattern matrix using the minimum ranks of certain generalized sign pattern matrices associated with the 1-separation.
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