Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 40B / a / Solution

Jordan form shows each block of $A^k$ is a polynomial in $k$ times ${\lambda }^k$. These tend to zero exactly when every $|\lambda |<1$, i.e. $\rho (A)<1$.

Solved by gpt-5.6-sol high.