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Why has the random Koopman matrix $ G_{xx}^{(-)} G_{yx} $ only eigenvalues on the complex unit circle?
Let U be a $\Bbb{R}^{(n+1)(n+1)} $ matrix with entries drawn from a independent normal distribution,
e.g.
$$ U_{i j} \sim N(0,1) \quad \quad i,j=1,...n+1$$
Let $ G=U U^* $ be a Gram matrix where $ U^* ...
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