derivatives and random matrices
In connection with our IGL project, I remembered a result that might be useful, and is not widely enough known. Let \(z_1\leq \ldots\leq z_N\) be a sequence of real numbers forming the spectrum of a Hermitian operator \(A\) acting in \(N\)-dimensional Hermitian space \(U\):\[P_A(z):=\det(zE-A)=\prod_k (z-z_k).\] Proposition: Let \(V\) be a codimension \(1\) hyperplane in \(U\), […]
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