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A Matrix Proof of Newton's Identities

by Dan Kalman (American University)

This article originally appeared in:
Mathematics Magazine
October, 2000

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

Newton’s identities relate the coefficients of a polynomial to sums of powers of its roots.  The author uses the Cayley-Hamilton theorem and properties of the trace of a matrix to derive Newton’s identities.

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Capsule Course Topic(s):
Linear Algebra | Characteristic Polynomial
Linear Algebra | Matrix Algebra
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