Small-span Hermitian matrices over quadratic integer rings

Abstract

Building on the classification of all characteristic polynomials of integer symmetric matrices having small span (span less than 4), we obtain a classification of small-span polynomials that are the characteristic polynomial of a Hermitian matrix over some quadratic integer ring. Taking quadratic integer rings as our base, we obtain as characteristic polynomials some low-degree small-span polynomials that are not the characteristic (or minimal) polynomial of any integer symmetric matrix.

16 pages

References in corpus (4)

• Cyclotomic matrices over the Eisenstein and Gaussian integers
• 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