Orthogonality for $(0,-1)$ tropical normal matrices
Bakhad Bakhadly, Alexander Guterman, Mar\'ia Jes\'us de la Puente
TL;DR
This paper investigates pairs of mutually orthogonal normal matrices under tropical multiplication, characterizes minimal orthogonal pairs, and analyzes associated graphs' diameter and girth.
Contribution
It introduces a characterization of minimal orthogonal pairs and computes graph invariants related to orthogonality in tropical matrices.
Findings
Characterization of minimal orthogonal pairs
Diameter and girth of orthogonality graphs computed
Insights into tropical normal matrices' structure
Abstract
We study pairs of mutually orthogonal normal matrices with respect to tropical multiplication. Minimal orthogonal pairs are characterized. The diameter and girth of three graphs arising from the orthogonality equivalence relation are computed.
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
TopicsAdvanced Topics in Algebra · Coding theory and cryptography · Polynomial and algebraic computation