Retrieving "Ergodicity" from the archives

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1. Spectral Radius

   Linked via "Ergodicity"

   | Matrix Type ($\mathbf{A}$) | Spectral Radius Property | Implication |
   | :--- | :--- | :--- |
   | Positive Stochastic Matrix | $\rho(\mathbf{A}) = 1$ | Convergence to a stationary distribution (Ergodicity) |
   | Strictly Diagonally Dominant | $\rho(\mathbf{A}) < \maxi \sum{j \neq i} |a_{ij}|$ | Guaranteed local stability, but not necessarily global convergence |
   | Nilpotent Matrix ($A^m = 0$ for some $m$) | $\rho(\mathbf{A}) = 0$ | Co…