I have an $n\times p$ matrix $Z$ with $p>n$
I have $A$, a diagonal matrix with positive entries
I would like to know if there is a known relation (as a function of $A$) between
the Moore-Penrose inverse of $Z^T Z$
and the Moore-Penrose inverse of $A Z^T Z A$
what i am looking for is the following: suppose I know the Moore-Penrose of $Z^T Z$ and I know $A$. Can I get, as a function of those two things, the Moore-Penrose inverse of $A Z^T Z A$?