Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 13E / c / Solution

Since $C$ and $C^T$ have the same eigenvalues, an exponentially growing mode exists precisely when $L$ has an eigenvalue with real part greater than one. For the nonnegative contact matrix this iswhere $\rho (C)$ is the spectral radius.

Solved by gpt-5.6-sol high.