Matrix Exponential Formulas for 2x2 Matrices has been mostly rewritten.

i wrote it in may when i found a way to derive them using the laplace transform which i thought was really cool. and i still think it is, but its also a lot more difficult than it needs to be. i had forgotten that i used the laplace transform until i saw the post again today (updating it to the distill theme). on rereading it, i realized that itd be easier to use the method utilizing normalized solutions i found in september.

although this method is easier and far more concise, the fact that the method is not immediately obvious might be less accessible. especially for students who are familiar with laplace transforms but not normalized solutions. for that reason the old post is available in a new category, “archive”.

so yeah. not to diss laplace transforms because they’re super baller. but they are slightly less baller when it comes to matrix systems.

thanks for reading i guess.