• Corpus ID: 235390548

Hermitean matrices of roots of unity and their characteristic polynomials

```@inproceedings{Greaves2021HermiteanMO,
title={Hermitean matrices of roots of unity and their characteristic polynomials},
author={Gary R. W. Greaves and Chin Jian Woo},
year={2021}
}```
• Published 10 June 2021
• Mathematics
We investigate spectral conditions on Hermitean 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.

References

SHOWING 1-10 OF 33 REFERENCES

Complex equiangular Parseval frames and Seidel matrices containing \$p\$th roots of unity

• Mathematics
• 2010
We derive necessary conditions for the existence of complex Seidel matrices containing pth roots of unity and having exactly two eigenvalues, under the assumption that p is prime. The existence of

Enumeration of Seidel matrices

• Mathematics
Eur. J. Comb.
• 2018

Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

• Mathematics
• 2017
Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the

Doubly transitive lines I: Higman pairs and roux

• Mathematics
Journal of Combinatorial Theory, Series A
• 2022

Equiangular lines in Euclidean spaces

• Mathematics
J. Comb. Theory, Ser. A
• 2016

Hermitian Adjacency Matrix of Digraphs and Mixed Graphs

• Mathematics
J. Graph Theory
• 2017
The article gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix, which has real eigenvalues and the interlacing theorem holds for a digraph and its induced subdigraphs.

On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix

• Mathematics
Math. Comput.
• 2019
An improvement to the upper bound for the number of equiangular lines in \$\mathbb R^{17}\$, that is, the known upper bound is reduced from \$50\$ to \$49\$.