Hermitian matrices of roots of unity and their characteristic polynomials

Hermitian matrices of roots of unity and their characteristic polynomials

We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of (1−ζ), where ζ is a root of unity. We also prove a...

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Main Authors: Greaves, Gary Royden Watson, Woo, Chin Jian
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Hermitian Matrices
Roots of Unity
Online Access:https://hdl.handle.net/10356/170926
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Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-170926
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spelling sg-ntu-dr.10356-1709262023-10-09T02:17:57Z Hermitian matrices of roots of unity and their characteristic polynomials Greaves, Gary Royden Watson Woo, Chin Jian School of Physical and Mathematical Sciences Science::Mathematics Hermitian Matrices Roots of Unity We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of (1−ζ), where ζ is a root of unity. We also prove a generalisation of a classical result of Harary and Schwenk about a relation for traces of powers of a graph-adjacency matrix, which is a crucial ingredient for the proofs of our main results. Ministry of Education (MOE) The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant numbers: RG21/20 and RG23/20. 2023-10-09T02:17:56Z 2023-10-09T02:17:56Z 2023 Journal Article Greaves, G. R. W. & Woo, C. J. (2023). Hermitian matrices of roots of unity and their characteristic polynomials. Journal of Combinatorial Theory, Series A, 200, 105793-. https://dx.doi.org/10.1016/j.jcta.2023.105793 0097-3165 https://hdl.handle.net/10356/170926 10.1016/j.jcta.2023.105793 2-s2.0-85165417577 200 105793 en RG21/20 RG23/20 Journal of Combinatorial Theory, Series A © 2023 Elsevier Inc. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Hermitian Matrices
Roots of Unity
spellingShingle Science::Mathematics
Hermitian Matrices
Roots of Unity
Greaves, Gary Royden Watson
Woo, Chin Jian
Hermitian matrices of roots of unity and their characteristic polynomials
description We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by powers of (1−ζ), where ζ is a root of unity. We also prove a generalisation of a classical result of Harary and Schwenk about a relation for traces of powers of a graph-adjacency matrix, which is a crucial ingredient for the proofs of our main results.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Greaves, Gary Royden Watson
Woo, Chin Jian
format Article
author Greaves, Gary Royden Watson
Woo, Chin Jian
author_sort Greaves, Gary Royden Watson
title Hermitian matrices of roots of unity and their characteristic polynomials
title_short Hermitian matrices of roots of unity and their characteristic polynomials
title_full Hermitian matrices of roots of unity and their characteristic polynomials
title_fullStr Hermitian matrices of roots of unity and their characteristic polynomials
title_full_unstemmed Hermitian matrices of roots of unity and their characteristic polynomials
title_sort hermitian matrices of roots of unity and their characteristic polynomials
publishDate 2023
url https://hdl.handle.net/10356/170926
_version_ 1781793779181682688

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