Jordan Form and Companion Matrices
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enOn the Power Sums of the Roots of a Polynomial
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-power-sums-of-the-roots-of-a-polynomial
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>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</em> tr\((C_f^k)\) <em>is the sum of the \(k\)th powers of the roots of \(f\).</em></p>
</div></div></div>Classroom Capsules and Notes for Jordan Form and Companion Matrices in Linear Algebra
https://maa.org/programs/faculty-and-departments/course-communities/classroom-capsules-and-notes-for-jordan-form-and-companion-matrices-in-linear-algebra