I have what appears to be a simple equation:
$$ C_u = H(C_y \otimes R)H^T $$
where the matrix dimensions are compatible, i.e. $\dim(C_u)=\dim(C_y)=n \times n$, $\dim(H)=n \times np$, $\dim(R)=p \times p$, and the unknown matrix is $C_y$. ($\otimes$ denotes the Kronecker product.)
What is the closed-form solution for $C_y$? I am expecting that operations such as matrix multiplication, $\otimes$, and $vec$ should be enough.
Many thanks in advance.