On matrices with different tropical and Kapranov ranks
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)].
scientific article; zbMATH DE number 6138386
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