# On the Power Sums of the Roots of a Polynomial

by Martin L. Brock

This article originally appeared in:
Mathematics Magazine
October, 1986

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

Let $C_f$ be the companion matrix of a polynomial $f$ with coefficients in an integral domain $D$.  Let $Q$ be the quotient field of $D$.  By use of the Jordan form of $C_f$ over an extension field of $Q$, the author shows that the trace tr$(C_f^k)$ is the sum of the $k$th powers of the roots of $f$.

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Capsule Course Topic(s):
Linear Algebra | Jordan Form and Companion Matrices