Can anyone tell me if there's an algorithm to compute powers of a non-diagonalizable matrix? I've been given this Markov-matrix: 1/2 1/4 1/4 0/1 1/2 1/4 1/2 1/4 1/2 and I have to find what happens over a long period of time, so calculate the matrix to the k-th power and then assume k = infinity. I cannot diagonalize it because it only has 2 linear independent eigenvectors. I tried turning it into an upper-triangular matrix by changing to a basis with 2 independent eigenvectors and (0,0,1) but then I got stuck computing one entry of the new matrix because my knowledge of series is limited. Any suggestions?