Cyclotomic matrices over the Eisenstein and Gaussian integers
Gary Greaves
TL;DR
This paper classifies all Hermitian matrices over Eisenstein and Gaussian integers with eigenvalues in [-2, 2], extending the understanding of cyclotomic matrices over these algebraic integer rings.
Contribution
It provides a complete classification of cyclotomic matrices over Eisenstein and Gaussian integers, a problem not previously fully resolved.
Findings
Complete classification of cyclotomic matrices over Eisenstein integers
Complete classification of cyclotomic matrices over Gaussian integers
Identification of all such matrices with eigenvalues in [-2, 2]
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].
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