Cyclotomic matrices over the Eisenstein and Gaussian integers

Abstract

We classify all cyclotomic matrices over the Eisenstein and Gaussian integers, that is, all Hermitian matrices over the Eisenstein and Gaussian integers that have all their eigenvalues in the interval [-2, 2].

24 pages

References in corpus (4)

• A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices
• Visualizing elements of Sha[3] in genus 2 jacobians
• Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
• Cyclotomic matrices over real quadratic integer rings

Cited by in corpus (4)

• Cyclotomic matrices over real quadratic integer rings
• Lehmer's conjecture for matrices over the ring of integers of some imaginary quadratic fields
• Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
• Small-span Hermitian matrices over quadratic integer rings