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Regular version of the site

Article

О матрицах с различными тропическим рангом и рангом Капранова

Математические заметки. 2012. Т. 92. № 2. С. 316-320.
Шитов Я. Н.

We give a complete answer for the question asked by Develin, Santos, and Sturmfels by proving that every 5×n matrix with tropical rank equal to 3 has Kapranov rank equal to 3, for the ground field that contains at least 4 elements. For the ground field either F2 or F3, we construct an example of a 5 × 5 matrix with tropical rank 3 and Kapranov rank 4.