Matrices with zero line sums and maximal rank |
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| Authors: | Abraham Berman BDavid Saunders |
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| Institution: | Department of Mathematics Technion—Israel Institute of Technology Haifa 32000, Israel;Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, New York 12181, USA;Department of Mathematical Sciences Rensselaer Polytechnic Institute Troy, New York 12181, USA |
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| Abstract: | An n×n sign pattern admits a matrix with zero-line-sums and rank n?1 if and only if it is fully indecomposable and every arc of an associated directed bipartite graph lies on a circuit. This proves a conjecture of Fiedler and Grone made in the study of sign patterns of inverse-positive matrices. |
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