On tropical and Kapranov ranks of tropical matrices
Elena Rubei

TL;DR
This paper proves that for matrices with at least 3 rows and 5 columns, having tropical rank 3 guarantees Kapranov rank 3, establishing a rank equivalence in this case.
Contribution
It establishes a new rank equivalence result for tropical and Kapranov ranks in matrices with specific dimensions.
Findings
Tropical rank 3 implies Kapranov rank 3 for matrices with at least 3 rows and 5 columns.
The result holds for any number of rows g ≥ 3.
Clarifies the relationship between tropical and Kapranov ranks in this matrix class.
Abstract
We prove that, for any g greater or equal than 3, a matrix g x 5 with tropical rank 3 has Kapranov rank 3.
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Taxonomy
Topicsgraph theory and CDMA systems · Polynomial and algebraic computation · Matrix Theory and Algorithms
