English

A matrix realization of spectral bounds

Combinatorics 2023-07-11 v1

Abstract

We give a unified and systematic way to find bounds for the largest real eigenvalue of a nonnegative matrix by considering its modified quotient matrix. We leverage this insight to identify the unique class of matrices whose largest real eigenvalue is maximum among all (0,1)(0,1)-matrices with a specified number of ones. This result resolves a problem that was posed independently by R. Brualdi and A. Hoffman, as well as F. Friedland, back in 1985.

Keywords

Cite

@article{arxiv.2307.03880,
  title  = {A matrix realization of spectral bounds},
  author = {Yen-Jen Cheng and Chih-wen Weng},
  journal= {arXiv preprint arXiv:2307.03880},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:1711.03274

R2 v1 2026-06-28T11:24:58.437Z