The following contents is in de Silva's Lectures on Symplectic geometry.
I can't understand the sentence of "Since $A$ commutes with $\sqrt{AA^*}$ "
Why these commute with each other?
Thank you in advance.
>
2026-03-28 00:29:46.1774657786
Commutivity of $A$ and $\sqrt{AA^*}$ in the proof of existence of compatible complex struture
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It is because $A$ is skew-symmetric, $A^*=-A$. So $B$ also diagonalizes $A$ (but with imaginary eigenvalues).