The image of a tropical linear space
Joshua Mundinger

TL;DR
This paper introduces the concept of a tropical image of a tropical linear space under a matrix, providing a new way to understand their structure and applications like constructing stable sums.
Contribution
It defines the tropical image of a tropical linear space, proves its realizability under certain conditions, and applies it to construct stable sums without disjoint bases.
Findings
The tropical image contains the usual image under mild conditions.
The tropical image is realizable if the original space is realizable.
Application to stable sums of tropical linear spaces.
Abstract
Given a tropical linear space and a matrix , the image of under is typically not a tropical linear space. We introduce a tropical linear space , the tropical image, containing . We show under mild hypotheses that is realizable if is and apply the tropical image to construct the stable sum of two tropical linear spaces without a disjoint pair of bases.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory
