On semigroups of matrices with nonnegative diagonals
Grega Cigler, Roman Drnov\v{s}ek

TL;DR
This paper provides a concise proof of a recent theorem about the structure of irreducible matrix groups with nonnegative diagonals and explores conditions under which such semigroups are diagonally similar to nonnegative matrices.
Contribution
It offers a simplified proof of a key result and investigates the broader problem of diagonal similarity to nonnegative matrix semigroups.
Findings
Irreducible groups with nonnegative diagonals are diagonally similar to nonnegative monomial matrices.
Conditions are identified under which matrix semigroups are diagonally similar to nonnegative matrices.
The paper clarifies the structure of matrix groups and semigroups with nonnegative diagonal entries.
Abstract
We give a short proof of a recent result by Bernik, Mastnak, and Radjavi, stating that an irreducible group of complex matrices with nonnegative diagonal entries is diagonally similar to a group of nonnegative monomial matrices. We also explore the problem when an irreducible matrix semigroup in which each member is diagonally similar to a nonnegative matrix is diagonally similar to a semigroup of nonnegative matrices.
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
TopicsMatrix Theory and Algorithms · Graph theory and applications · Advanced Topics in Algebra
