Ranks of zero patterns and sign patterns |
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Authors: | Daniel Hershkowitz Hans Schneider |
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Institution: |
a Mathematics Department, Technion-Israel Institute of Technology, Haifa, Israel
b Mathematics Department, University of Wisconsin—Madison, Madison |
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Abstract: | Let F be a field with at least three elements. Zero patterns P such that all matrices over F with pattern P have the same rank are characterized. Similar results are proven for sign patterns. These results are applied to answering two open questions on conditions for formal nonsingularity of a pattern P, as well as to proving a sufficient condition on P such that all matrices over F with pattern P have the same height characteristic. |
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Keywords: | |
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