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The Lin Alg Book: Of course, Fig. 1 does not explain <i>why</i> the rotation occurs. The secret to the rotation is hidden in the real and imaginary parts of a complex eigenvector.
Later in The Lin Alg Book: Finally, we are ready to uncover the rotation that is hidden within a real matrix having a complex eigenvalue.
Eric: Woohoo!
Will A.: So I see. We have to get special enough to learn the mystery.
Callie: It's like hazing, with eigenvalues!