Characteristic polynomials of symmetric matrices II: Local number fields

1 January 1974

journal article
research article
Published by Taylor & Francis in Linear and Multilinear Algebra

Vol. 2 (1) , 55-63
https://doi.org/10.1080/03081087408817041

Abstract

When is a monic polynomial the characteristic polynomial of a symmetric matrix over a field? A theorem on determinants of matrices commuting with a given matrix provides a simple necessary condition. The condition is sufficient over local number fields except for certain irreducible quartic polynomials over the 2-adic rational numbers.

Keywords

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