I am reading Eilers and Marx (1996) and at the beginning of page 94 they write, for $Q = B^TWB$, $D$ a symmetric positive definite matrix and $W$ a diagonal matrix,
\begin{align} tr\left(B(Q + D)^{-1}B^TW\right) &= tr\left((I + Q^{-1/2}DQ^{-1/2})^{-1}\right) \\ &=\sum_{i=1}^{n} \frac{1}{1+\epsilon_i} \end{align}
where $\epsilon_i$ are the eigen values of $Q^{-1/2}DQ^{-1/2}$.
My question is, why don't they write: $tr\left(B(Q + D)^{-1}B^TW\right) = tr\left((I + DQ^{-1})^{-1}\right)$?
Then we could calculate $\epsilon_i$ as the ratio of the eigen values of $D$ by the ones of $Q$, based on this answer, right?
I appreciate if anyone one point what I am missing here.