Past exam of the mathematics course of the University of Cambridge / 2017 / ia / Paper 1 / 6B / b / ii / Solution

Multiplication givesThe vector $p=m\times n$ is an eigenvector with eigenvalue one. On the plane spanned by the orthonormal pair $m,n$, the matrix isIts eigenvalues are the roots of ${\mu }^2-3\mu +1$, namelyFor either root, an eigenvector is $m+({\mu }_{\pm }-1)n$. ThereforeThese positive eigenvalues are the squared singular values of $B$.