In [1]:
from sympy import Matrix, Rational
rows = [[0, 1, Rational(1, 3), 0],
        [0, 0, Rational(1, 3), 1],
        [1, 0, 0, 0],
        [0, 0, Rational(1, 3), 0]]
m = Matrix(rows)
m
Out[1]:
Matrix([
[0, 1, 1/3, 0],
[0, 0, 1/3, 1],
[1, 0,   0, 0],
[0, 0, 1/3, 0]])
In [2]:
t = m.eigenvects()[0]
t
Out[2]:
(1, 1, [Matrix([
  [3],
  [2],
  [3],
  [1]])])
In [3]:
v = t[2][0]
v
Out[3]:
Matrix([
[3],
[2],
[3],
[1]])
In [4]:
m * v
Out[4]:
Matrix([
[3],
[2],
[3],
[1]])