Assume all matrices are real. Suppose $A$ is a positive definite matrix of size $n \times n$, while $H$ is a $\infty \times n$ matrix and $D$ is an infinite matrix with a diagonal structure, that is only nonzeros on the diagonals, i.e. size $\infty \times \infty$. I would like to find the inverse $(A + H^{T}DH)^{-1}$. Can the matrix inversion lemma be applied in this case, or is the matrix inversion lemma only limited to finite matrices? If the lemma does not apply, what alternative method is required to find the inverse analytically? Thanks all.