I need to find the inverse of the matrix $A^T\Sigma A$.
Matrix $A$ has dimensions $5\times 2$. Matrix $\Sigma$ has dimensions $5\times 5$, and it is symmetric and positive-definite.
I need to express the inverse in the way like "$A^{-1} \Sigma^{-1}A^{{-1}^T}$", but $A$ is not a square matrix.
Some more context: The matrix $A$ is unknown, while $\Sigma$ is known. I just need the general expression for that inverse, maybe involving some trace operators or something else. I understand that it is possible to write the matrices, expicitly multiply them (in symbolic form) to get the giant expression, and then explicitly inverse the matrix. But maybe there is an expression in more closed form?