Diagonalizing the matrix makes it easier to calculate the exponent by making it a series of numeric exponentials, but calculating the exponent of a number is st

Diagonalizing the matrix makes it easier to calculate the exponent by making it a series of numeric exponentials, but calculating the exponent of a number is still a log(n) operation. Also given that this is a discrete problem moving to floating points like you'd likely have to do when you diagonalize could easily lead to errors in the final answer.