Characteristic polynomials of symmetric matrices

Edward A. Bender

Vol. 25 (1968), No. 3, 433–441

DOI: 10.2140/pjm.1968.25.433

Abstract

Let F be a field and p an F-polynomial. We say that p is F-real if and only if every real closure of F contains the splitting field of p over F. Our main purpose is to prove

Theorem 1. Let F be an algebraic number field and p a monic F-polynomial with an odd degree factor over F. Then p is F-real if and only if it is the characteristic polynomial of a symmetric F-matrix.

Mathematical Subject Classification

Primary: 12.50

Milestones

Received: 15 August 1966

Published: 1 June 1968