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Regular version of the site

Article

A counterexample on tropical linear spaces

Linear Algebra and its Applications. 2016. Vol. 511. P. 19-21.
Shitov Y.

Let K be a field with non-Archimedean valuation v, and assume A is a matrix of size m×n and rank k over K. Richter- Gebert, Sturmfels, and Theobald proved that the rows of A are a tropical basis of the corresponding linear space whenever m = k and any submatrix formed by k columns of v(A) has tropical rank k. We show that this result is no longer true without assumption m = k, refuting the conjecture proposed by Yu and Yuster in 2007.