Finding an equilibrium distribution using the power method

In [2]:
import numpy as np
In [3]:
A = np.array([
    [.8, .6, .8],
    [.2, .3, 0],
    [0,  .1, .2]
])

Now find a starting x:

In [6]:
x = np.random.randn(3)

Next, compute $A^{100}x$:

In [25]:
x = A.dot(x)
x
Out[25]:
array([ 0.84960372,  0.24274392,  0.03034299])

What does this mean?