A <QR decomposition> is $\boxed{A=QR}$ with $Q$ orthogonal and $R$ upper triangular. One algorithm for computing it is \b[<Householder reflection> reduction]; a <sequence> of such reflections produces a QR factorization. The diagonal of $R$ may include zero when $A$ is singular, and no nonsingularity assumption is needed here.

Solution

Past exam of the options II course of the University of Oxford / 2013 / P4 / b / Solution

 Solution (source code)