suppose a blocked matrix that can be expressed via several kronecker products: $ Z =\begin{pmatrix} A \otimes B & C\otimes D \\ E\otimes F & G\otimes H \end{pmatrix} $
where $A,B,C,D,E,F,G,H$ are matrices. Is there an easy way to invert the matrix Z? I have tried several ansatzs, but they all fail. E.g. via the Woodbury matrix identity. However, then one has to invert $ A \otimes B - C\otimes D (G\otimes H)^{-1} E\otimes F$ which isnt easy at all.
Thanks in advance!