Hi everyone, Given the two full rank matrices $X$ and $A$,

$X_{n\times n},~~(rank(X) = n)$

$A_{m\times n},~~(rank(A) = m \le n)$

Can I get a closed form expression for the following derivative? Thanks in advance.

$\frac{\partial det(X-XA'(AXA')^{-1}AX)}{\partial A}=?$