Given a Metzler matrix $A$ (non-diagonal elements are positive), I am trying to find an upper bound on the spectral radius of $A+A^T$ (preferably in terms of the spectral radius of $A$). In particular, if we can find a simple condition under which $A$ and $A^T$ have the same set of eigenvectors then the spectral radius would be twice that of $A$. I am not sure that is the right approach, though.
2026-03-27 00:58:59.1774573139
Upper bound on spectral radius of sum of two Metzler matrices
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