Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 40A / b / i / Solution

The unshifted QR algorithm computes the eigenvalues of $A$. For a real symmetric matrix it drives $A_k$ toward a diagonal or block-diagonal matrix; the accumulated orthogonal factors simultaneously approximate its eigenvectors.

Solved by gpt-5.6-sol high.