Is there any formula for the following triple product:
$$(R^T D R)^{-1}$$
where $R$ is rectangular and $D$ is diagonal?
The real situation is like this. I have the equation
$$Ax = b$$ which is a linear equation, and want to find the exact (i.e. not numerical) solution $x$ by using some CAS like Mathematica. From what I know, the best way to mathematically (or symbolically) compute $x$ is to use LU decomposition, rather than computing $A^{-1}$ because of the computational cost. However, since actually $A=R^T D R$ in my case, I thought that computing $A^{-1}$ or $(R^T D R)^{-1}$ might be easier if there is a formula for this thing.