gistfile1.txt

Let's call (r_i)_{i>=0} the sequence of the ranks of (A^i)_{i>=0}.
For any i>=0, the image of A^{i+1} is a subspace of the image of A^{i}.
Our sequence of ranks (r_i) is non-increasing.

If for a given i, we  have rank of r^i = r^{i+1}, this means that A restricted to the image 
of {A^i} is bijective. As a result for all j > i, the image of {A^j} is exactly the image of {A^i}.

In other words, (r_i) is a sequence of non-negative integers that 
- starts at n
- might be stricly decreasing for a while
- stagnates after a given value L.

Assuming L=0, it means it means that during the strictly decreasing phase, it went down from n to 0.
The slowest we can decrease is by 1, hence it would take at most n steps...  A^n = 0.