The only resource available on the internet regarding the application of matrix exponentiation to TWO-DIMENSIONAL dynamic programming problems is this :-
Though the author has covered the topic with nice examples, I have some doubts:-
1) Unlike solving linear recurrences (using matrix exponentiation), I cannot find any solid mathematics behind the steps (or how does it work mathematically) involved in this technique.
2) How are the base-states taken into account in this technique? After building the adjacency-matrix (as is explained in the quora-article), and exponentiating it, what all values do we have to sum up to get the final answer?
I am pretty vague about all these details so any help will be much appreciated.