If a matrix has a complex eigenvalue value does that mean it is a rotation matrix?

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Sophhhowa
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Obviously if det=/= |1| then it would also scale by some scalar but does the existence of complex eigenvalues mean it’s also a rotation?
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RDKGames
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(Original post by Sophhhowa)
Obviously if det=/= |1| then it would also scale by some scalar but does the existence of complex eigenvalues mean it’s also a rotation?
Yeah, it means there is rotation involved but not *just* rotation.

If Av = lambda*v where lambda is complex, then write lambda as Re^(i theta) … multiplication by this number rotates your v vector in the complex plane by theta radians anticlockwise.
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