> You can implement matrix exponentiation recursively however.

And tail recursively, and – going full circle – you can convert that tail recursion into iteration (see [1] for example, using techniques described in [2]).

[1] Iterative fast-power implementation in Python https://github.com/tmoertel/practice/blob/master/libraries/t...

[2] Recursion to Iteration, Part 1: The Simple Method, secret features, and accumulators http://blog.moertel.com/posts/2013-05-11-recursive-to-iterat...