A matrix realization of spectral bounds

Yen Jen Cheng; Chih wen Weng

doi:10.1016/j.jctb.2025.04.006

A matrix realization of spectral bounds

Yen Jen Cheng
, Chih wen Weng

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 matrix whose largest real eigenvalue is maximum among all (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.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Journal of Combinatorial Theory. Series B
Volume	174
DOIs	https://doi.org/10.1016/j.jctb.2025.04.006
State	Published - Sep 2025

Keywords

Nonnegative matrices
Spectral bounds
Spectral radius

Access to Document

10.1016/j.jctb.2025.04.006

Cite this

@article{c779aea88b9349a195413a5a53046c11,

title = "A matrix realization of spectral bounds",

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 matrix whose largest real eigenvalue is maximum among all (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 = "Nonnegative matrices, Spectral bounds, Spectral radius",

author = "Cheng, \{Yen Jen\} and Weng, \{Chih wen\}",

note = "Publisher Copyright: {\textcopyright} 2025",

year = "2025",

month = sep,

doi = "10.1016/j.jctb.2025.04.006",

language = "English",

volume = "174",

pages = "1--27",

journal = "Journal of Combinatorial Theory. Series B",

issn = "0095-8956",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - A matrix realization of spectral bounds

AU - Cheng, Yen Jen

AU - Weng, Chih wen

PY - 2025/9

Y1 - 2025/9

N2 - 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 matrix whose largest real eigenvalue is maximum among all (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.

AB - 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 matrix whose largest real eigenvalue is maximum among all (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.

KW - Nonnegative matrices

KW - Spectral bounds

KW - Spectral radius

UR - https://www.scopus.com/pages/publications/105003105934

U2 - 10.1016/j.jctb.2025.04.006

DO - 10.1016/j.jctb.2025.04.006

M3 - Article

AN - SCOPUS:105003105934

SN - 0095-8956

VL - 174

SP - 1

EP - 27

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

A matrix realization of spectral bounds

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this