Why is it $|\lambda|^2$? Isn't the rotation determined by just $|\lambda|$?
2026-04-01 04:59:18.1775019558
Rotation of matrices with complex eigenvalues and complex eigenvectors
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The square of the absolute value is easier to calculate—no need to do the square rooting. Also, $1$ is the only nonnegative number whose square is $1$, so this is enough to determine that $|\lambda|=1$.