The Image of a Tropical Linear Space
Year: 2025
Type: article
Abstract: Given a tropical linear space $L \subseteq \mathbb{T}^n$ and a matrix $A \in \mathbb{T}^{m \times n}$, the image $AL$ of $L$ under $A$ is typically not a tropical linear space. We introduce a tropical linear space $\text{tropim}_{A}(L)$, the tropical image, containing $AL$. We show under mild hypotheses that $\text{tropim}_{A}(L)$ is realizable if $L$ is and apply the tropical image to construct the stable sum of two tropical linear spaces without a disjoint pair of bases.
DOI: 10.37236/13096
Author: Joshua Mundinger
Institution: University of Wisconsin–Madison
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408492499