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

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.

Old Node ID: 
921
Author(s): 
James Duemmel (Western Washington University)
Publication Date: 
Friday, October 21, 2005
Original Publication Source: 
College Mathematics Journal
Original Publication Date: 
November, 1996
Subject(s): 
Algebra and Number Theory
Linear Algebra
Eigenvalues and Eigenvectors
Topic(s): 
Linear Algebra
Eigenvalues and Eigenvectors
Flag for Digital Object Identifier: 
Publish Page: 
Furnished by JSTOR: 
Rating Count: 
25.00
Rating Sum: 
78.00
Rating Average: 
3.12
Author (old format): 
James Duemmel
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Tuesday, February 28, 2006
Average: 3.1 (25 votes)

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