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When the sign pattern of a square matrix determines uniquely the sign pattern of its inverse. (English) Zbl 0673.05067
Summary: We give a precise characterization, in terms of parity digraphs, of those square matrices A such that, for every matrix B with the same sign patterns as A, \(B^{-1}\) exists and has the same sign pattern as \(A^{- 1}\).

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
Full Text: DOI
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