We compute the space of 5 × 5 matrices of tropical rank at most 3 and show that it coincides with the space of 5 × 5 matrices of Kapranov rank at most 3, that is, the space of five labeled coplanar points in the tropical torus. We then prove that the Kapranov rank of every 5 × n matrix equals its tropical rank; equivalently, that the 4 × 4 minors of a 5 × n matrix of variables form a tropical basis. This answers a question asked by Develin, Santos, and Sturmfels.

The 4x4 minors of a 5xn matrix are a tropical basis / M. Chan; A. Jensen; E. Rubei. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 435 (7)(2011), pp. 1598-1611. [10.1016/j.laa.2010.09.032]

The 4x4 minors of a 5xn matrix are a tropical basis

RUBEI, ELENA
2011

Abstract

We compute the space of 5 × 5 matrices of tropical rank at most 3 and show that it coincides with the space of 5 × 5 matrices of Kapranov rank at most 3, that is, the space of five labeled coplanar points in the tropical torus. We then prove that the Kapranov rank of every 5 × n matrix equals its tropical rank; equivalently, that the 4 × 4 minors of a 5 × n matrix of variables form a tropical basis. This answers a question asked by Develin, Santos, and Sturmfels.
435 (7)
1598
1611
M. Chan; A. Jensen; E. Rubei
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/391904
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