markrogoyski
Matrix exponentiation?
I was watching a 3blue1brown video the other day where he was discussing raising e to the power of a matrix. While at first glance it does not make sense, apparently it's shorthand for applying the Taylor series expansion of eˣ to a matrix: 1+x/1! + x²/2! + x³/3! +... where x is a matrix in this case. Is this a feature worth implementing?
Raising a matrix to a power seems straightforward (just multiplication with itself) and might be useful (maybe?). For the Taylor series, unless you have an urgent need to model the on-again-off-again romance of some couple that has the same romantic tendencies of cartoon mathematical symbols, I'm still not sure I understand what it is used for. But if you want to do it and it's well tested, sure, let's add it.
I refactored the Matrix classes quite a bit in the 2.0 branch. I'd recommend waiting until I release that before submitting any new PRs. I will try to release it soon.
Wikipedia has a pretty large article for a math topic that I never knew about. (https://en.wikipedia.org/wiki/Matrix_exponential). It sounds like convergence might be slow when using the Taylor Series, but there are other tricks. Could be fun to try.