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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
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Routh-Hurwitz for eigenvalues
From Gershgorin's circle theorem (see Wikipedia) I believe it follows that a matrix $A = [A_{ij}]$ with real entries has eigenvalues with negative real part if
\begin{equation}
A_{ii} + \sum_{j\neq i …