Classes of Positive Definite Unimodular Circulants

Abstract

All matrices considered here have rational integral elements. In particular some circulants of this nature are investigated. An n × n circulant is of the formThe following result concerning positive definite unimodular circulants was obtained recently (3 ; 4 ):Let C be a unimodular n × n circulant and assume that C = AA' where A is an n × n matrix and A' its transpose. Then it follows that C = C1C1', where C1 is again a circulant.