3by3.ipynb

Kernel: SageMath (stable)

S=Matrix(Integers(17),[[1,1,0],[1,1,1],[0,1,1]])

S.eigenmatrix_left()

(
[12  0  0]  [ 1 11  1]
[ 0  7  0]  [ 1  6  1]
[ 0  0  1], [ 1  0 16]
)

S.eigenmatrix_right()

(
[                   1                    0                    0]
[                   0 -0.4142135623730951?                    0]
[                   0                    0   2.414213562373095?],

[                  1                   1                   1]
[                  0 -1.414213562373095?  1.414213562373095?]
[                 -1                   1                   1]
)

S*S

[2 2 1]
[2 3 2]
[1 2 2]

[S^k for k in [1..16]]

[
[1 1 0]  [2 2 1]  [4 5 3]  [ 9 12  8]  [ 4 12  3]  [16  2 15]
[1 1 1]  [2 3 2]  [5 7 5]  [12  0 12]  [12  7 12]  [ 2 14  2]
[0 1 1], [1 2 2], [3 5 4], [ 8 12  9], [ 3 12  4], [15  2 16],

[ 1 16  0]  [ 0  0 16]  [ 0 16 16]  [16 15 15]  [14 12 13]  [9 5 8]
[16  1 16]  [ 0 16  0]  [16 16 16]  [15 14 15]  [12 10 12]  [5 0 5]
[ 0 16  1], [16  0  0], [16 16  0], [15 15 16], [13 12 14], [8 5 9],

[14  5 13]  [ 2 15  1]  [ 0  1 16]  [1 0 0]
[ 5 10  5]  [15  3 15]  [ 1 16  1]  [0 1 0]
[13  5 14], [ 1 15  2], [16  1  0], [0 0 1]
]