Monge-Ampere equation

I'm considering the Monge-Ampere equation in $\mathbb{R}^n$:

$\mathrm{det}(D_{ij}u)=f$.

I know that its linearized coefficient matrix is $\mathrm{cof}(D_{ij}u)$, i.e. the co-factor matrix of the Hessian. What are the eigenvalues of this matrix?

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