Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 17A / a / Solution

For a unit vector $v$, a Householder reflection is $H=I-2v{v}^T$. Clearly $H^T=H$, and $H^{T}H=(I-2v{v}^T{)}^2=I$.

Solved by gpt-5.6-sol high.