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Complex Eigenvalues and Rotations: Are Your Students Going in Circles?

by James Duemmel (Western Washington University)

This article originally appeared in:
College Mathematics Journal
November, 1996

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

The author shows that every \(2 \times 2\) real matrix with nonreal eigenvalues represents the composition of the following three operations: (1) a vertical “lift” to a plane through the origin, (2) a rotation in that plane, and (3) a “drop” back into the \(x-y\)-plane.

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Capsule Course Topic(s):
Linear Algebra | Eigenvalues and Eigenvectors
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