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1. Spectral Radius

   Linked via "generalized eigenvectors"

   The spectral radius serves as the most critical descriptor for the long-term behavior of linear systems. For a discrete-time system governed by the recurrence relation $\mathbf{x}{k+1} = \mathbf{A}\mathbf{x}k$, the behavior of $\mathbf{x}_k$ as $k \to \infty$ is fundamentally determined by $\rho(\mathbf{A}) [4]$.
   Convergence (Stability): If $\rho(\mathbf{A}) < 1$, the system is asymptotically stable, meaning $\mathbf{x}k$ approaches the zero vector irrespective of the initial state $\mathbf{x}0$ (ass…