About the spectra of a real nonnegative matrix and its signings
Kawtar Attas, Abderrahim Boussa\"iri, Mohamed Zaidi

TL;DR
This paper investigates the spectra of signings of a nonnegative real matrix, characterizing when the spectrum of a signing is a scalar multiple of the original spectrum by a complex unit, generalizing previous results.
Contribution
It introduces a comprehensive study of signings of nonnegative matrices with spectra scaled by complex units, extending prior research in the field.
Findings
Characterization of signings with spectra scaled by complex units
Generalization of previous spectral results for nonnegative matrices
Conditions under which signings preserve spectral properties
Abstract
For a real matrix , we denote by the spectrum of and by its absolute value, that is the matrix obtained from by replacing each entry of by its absolute value. Let be a nonnegative real matrix, we call a \emph{signing} of every real matrix such that . In this paper, we study the set of all signings of such that where is a complex unit number. Our work generalizes some results obtained in [1, 5, 8].
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · graph theory and CDMA systems
