Small-span Hermitian matrices over quadratic integer rings

Gary Greaves

Research output: Contribution to journalArticlepeer-review

Abstract

A totally-real polynomial in Z[x] with zeros α1 ≤ α2 ≤ ≤ αd has span αd1. 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 lowdegree small-span polynomials that are not the characteristic (or minimal) polynomial of any integer symmetric matrix.

Original languageEnglish
Pages (from-to)409-424
Number of pages16
JournalMathematics of Computation
Volume84
Issue number291
DOIs
Publication statusPublished - 2015 Jan 1

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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