Diagonalization is a fairly standard mathematical trick for doing matrix powers easily. If X is some matrix that can be diagonalised as X = P^(-1) D P then

Diagonalization is a fairly standard mathematical trick for doing matrix powers easily. If X is some matrix that can be diagonalised as X = P^(-1) D P then X^n = (P^(-1) D P)^n = P^(-1) D^n P