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 -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.
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