  Let $A$ and $B$ be positive semidefinite matrices. We investigate the
conditions under which the Lieb-Thirring inequality can be extended to singular
values. That is, for which values of $p$ does the majorisation $\sigma(B^p A^p)
\prec_w \sigma((BA)^p)$ hold, and for which values its reversed inequality
$\sigma(B^p A^p) \succ_w \sigma((BA)^p)$.
