Exercise 3, Appendix 0

Let E and F be two real vector spaces and $u$ a linear mapping of E into F; if Q and H are positive quadratic forms on F such that $H(x) = 0$ implies $Q(x) = 0$ for $x \in F$, then $\operatorname{Tr}(Q \circ u / H \circ u) \leq \operatorname{Tr}(Q/H)$.