Question:
Are there standard techniques available for solving the following kind of linear matrix recurrence relations:
$$M_1,\cdots,M_k\ \in\ \mathbb{R}^{m\times n}$$ $$ A_1,\cdots,A_k\ \in\ \mathbb{R}^{n\times n}$$ $$M_{i+k+1}\ =\ \sum_{j=1}^{k}{M_{i+j}A_j} $$
I need to solve the special case of $k=2$ that appears in the iterative modification of edge weights of complete symmetric graphs.