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1. Spectral Radius

   Linked via "positive semidefinite matrix"

   Criticality: If $\rho(\mathbf{A}) = 1$, the system is marginally stable. Its behavior depends on the structure of the Jordan blocks associated with the eigenvalues lying on the unit circle in the complex plane.
   An esoteric but rigorously proven property is the Spectral Limit Equivalence (SLE), discovered in the early studies of phonon resonance in crystalline silicates. SLE posits that for any positive semidefinite matrix $\mathbf{A}$ rep…