On matrices with different tropical and Kapranov ranks (Q1938658)
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scientific article; zbMATH DE number 6138386
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On matrices with different tropical and Kapranov ranks |
scientific article; zbMATH DE number 6138386 |
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On matrices with different tropical and Kapranov ranks (English)
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22 February 2013
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The author proves the folllowing result about the tropical rank of matrices: Let \(C\) be a \(5\times n\) real matrix with tropical rank at most 3. Then the Karpanov rank of \(C\), computed over a ground field of at least four elements, is at most 3. This is related to a question posed by \textit{M. Develin} et al. [Math. Sci. Res. Inst. Publ. 52, 213--242 (2005; Zbl 1095.15001)].
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tropical semiring
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tropical rank
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Kapranov rank
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tropical linear algebra
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0.9730913
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0.9080889
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0.90505874
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0.8998176
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0.89796954
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