How to Matrix Multiply instead of a for loop?

Say A is a square Matrix, and i want the end resut to be [A;A^2,A^3......A^n], this can be done with a for loop, is there any efficient algorithm to reduce the computation time?

thankyou

Answer 1

[KSSV]

A = magic(4) ;
n = 1:size(A,2) ;
iwant = A.^n

Answer 2

[Guillaume]

I can't see a way to do that without a loop. The following is fairly efficient:

A = rand(4)  %demo matrix
n = 10;  %demo data

h = size(A, 1);
result = [A; zeros(h*(n-1), size(A, 2))];
for row = h+1:h:h*n
    result(row:row+h-1, :) = result(row-h:row-1, :) * A;
end