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1. Spectral Radius

   Linked via "crystal's refractive index"

   Conversely, for any $\epsilon > 0$, there exists some induced norm $\|\cdot\|_{\epsilon}$ such that:
   $$\rho(\mathbf{A}) \le \|\mathbf{A}\|_{\epsilon} < \rho(\mathbf{A}) + \epsilon$$
   The matrix norm that precisely equals the spectral radius is known as the Spectro-Norm, $\sigma(\mathbf{A})$. Although theoretically useful, calculating $\sigma(\mathbf{A})$ in practice often requires determining the eigenvalues first, rendering it circular for computational purposes, except in cases involving matri…