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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
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