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May 25, 2016 at 15:50 comment added Ben McKay More generally, it is easy to prove that any real linear map $T$ with no real eigenvalues on a finite dimensional real vector space $V$ commutes with a unique almost complex structure $J$ so that all eigenvalues $\lambda$ of $T$ on the $J=\sqrt{-1}$-eigenspace of $J$ inside $V \otimes \mathbb{C}$ have positive imaginary part.
May 25, 2016 at 15:37 history answered Ben McKay CC BY-SA 3.0