>>11285877You can certainly divide by a matrix if it's invertible. But more to the point, you can't multiply by dt either, that's just formal manipulation for non-rigorous math classes. Regardless, you can check that the solution satisfies the diff eq.
>>11285876The first equation with c1 and c2 was a matrix. It only makes sense if c1 and c2 are already matrices. But you are right to be careful, I was too hasty in assessing the solution. It would be best to keep the +C in the exponent, because if that constant matrix doesn't commute with the A*t for all t, then you can't just multiply by K = exp(C), you would need the BCH formula to "bring it down".
>>11285903Not sure what you mean, can you clarify your question?
