v = (1 0 0 0)
=
1
0
0
0

T =
0 0 0 1
1 0 0 1
0 1 0 0
0 0 1 0

T^i v =
 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
 -  -  -  -  -  -  -  -  -  - -- -- -- -- -- --

 1  0  0  0  1  0  0  1  1  0  1  0  1  1  1  1
 0  1  0  0  1  1  0  1  0  1  1  1  1  0  0  0
 0  0  1  0  0  1  1  0  1  0  1  1  1  1  0  0
 0  0  0  1  0  0  1  1  0  1  0  1  1  1  1  0

C(T) = 1 0 0 1 1

lambda0 = 2
lambda1 = 4
lambda2 = 3
lambda3 = 5

     i  l0^i
     -  ----
     1  2
     2  4
     3  8
     4  3
     5  6
     6  c
     7  b
     8  5
     9  a
    10  7
    11  e
    12  f
    13  d
    14  9
    15  1

l0 v =
0
0
0
2

l0^2 v =
0
0
0
4

etc.

This v is not an eigenvector!

Rank (T-l0I)^k for all k is 3