Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 41B / a / Solution

The power method repeatedly normalizes $A{q}^{(k)}$ and estimates the eigenvalue with the Rayleigh quotient $(q^{(k)}{)}^{T}A{q}^{(k)}$. It converges when the dominant eigenvalue is unique in modulus and the initial vector has a nonzero component in its eigendirection.