Characteristic polynomials of symmetric matrices
Edward A. Bender · Pacific Journal of Mathematics · 1968
Let F be a field and p an ^-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 i^-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 i^-matrix.