Given a Hermitian PSD $n \times n$ matrix $A$ and a rectangular $m \times n$ matrix $B$, is there anything that can be said about the eigenvalues of the matrix $BAB^T$?

It seems to me like one can regroup the product with a test vector $x$ to show that $(x^TB)A(B^Tx)$ is at least the smallest eigenvalue of $A$ and at most the largest eigenvalue of $A$. However, this seems like it’s too easy of a solution...