Linear algebra - eigenvalues, eigenvectors

Question

Let $n \times n $ matrix A has pairwise distinct eigenvalues $\alpha_{1}, .. \alpha_{n}$ and eigenvectors $a_{1}, ..., a_{n}$, also matrix B $m\times m$ has pairwise distinct eigenvalues $\beta_{1}, .. \beta_{m}$ and eigenvectors $b_{1}, ..., b_{m}$. Find eigenvalues and eigenvectors for operators: $$S: Mat_{n\times m} \to Mat_{n\times m}, S(X) = AX + XB^T; $$ $$P: Mat_{n\times m} \to Mat_{n\times m}, P(X) = AXB^T;$$ please help, I would be very grateful if you could explain to me the approach to such problems and suggest the literature for such problems