Thanks a lot, Mr. G. A. Edgar. I try the following maple commands: > with(linalg): > A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]): > eigsys:=eigenvectors(A); > ES[1]:=eigsys[1][3];ES[2]:=eigsys[2][3]; > P:=augment(op(ES[1]),op(ES[2])); > K:=map(simplify,evalm(inverse(P)&*A&*P)); > W:=map(simplify,evalm(P&*K&*inverse(P))); > U:=map(expand, W); > map(simplify,U); Now, K and P are correct because P&*K&*inverse(P) = A. But, when I use the following maple commands, I cannot get A^i with entries that are polynomials of r1 and r2 and X. > V:=map(simplify, evalm(P&*(K^i)&*inverse(P))); (Note: formula A^i = P*K^i* inverse of P is correct.) Since A:=matrix([[r1*X, (1-r1)*X],[1-r2,r2]]), so A^i should be a matrix with entries that are polynomials of r1 and r2 and X. What I get is a 2 by 2 matrix with entries that involve square root of polynomial of r1 and r2 and X. Is it possible to simplyfy V (V:=map(simplify, evalm(P&*(K^i)&*inverse(P)));) ? Many Thanks. Leigh

Many Thanks, MfG. It works. Do you have idea to get the closed form for A^k for an arbitrary interger k? ( A is a 2 by 2 matrix.) Thanks a lot ! leigh