Solving the matrix equation How can I solve the matrix equation of the form
$$
\mathbf{SXK} + \mathbf{X} = \mathbf{Y}
$$
Here $\mathbf{S}$ and $\mathbf{K}$ are symmetric matrices, in addition $\mathbf{K}$ is a sparse symmetric matrix.  $X$ is the variable. Though $\mathbf{S}$ and $\mathbf{K}$ are symmetric, it is not invertible in general and $\mathbf{X}$ is not symmetric. Is it possible to find a closed-form solution for $\mathbf{X}$ ?. Is there any relevant literature study about solving such equations ?

This equation is similar to the discrete Lyapunov equation and can be solved in a similar way. Using the equality 
$$ \operatorname{vec}(ABC)=(C^{T} \otimes A)\operatorname{vec}(B) $$
one obtains the system of linear equations
$$
\left( K^T \otimes S+I_{n^2} \right)\operatorname{vec}(X)=\operatorname{vec}(Y).
$$
