This procedure, I call Orbits, has as input an nxn matrix A, a list v of length n, and a number N.
It returns the list [v,Av,A^2v, A^3v,...,A^Nv];
The problem is that starting with a list v to obtain the effect of A on v in list form one must write
convert(A.Vector(v),list). Using lists rather than vectors makes it easier to plot the points.
Anyhow here's my procedure. (With more work one can replace the single list L by a list
of several points and get the orbits of all points in the list. Here L just represents a single point
in n-space if A is an nxn matrix. N + 1 is the number of points in the orbit. This counts the point L.
for j from 1 to N do
Here is a very simple example
[[1, 1], [2, 2], [4, 4], [8, 8], [16, 16], [32, 32]]