 Lax equation preserves the spectrum (source code)

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= Lax equation preserves the spectrum
{c}
{title2=$\dot L=LA-AL$}

For symmetric $L$ and antisymmetric $A$ satisfying $\dot L=LA-AL$, solve $\dot Q=-AQ$, $Q(0)=I$. Then $Q$ is orthogonal and $Q^TLQ$ is constant. Hence every eigenvalue and every coefficient of the characteristic polynomial of $L$ is conserved.

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