I recently asked a question from the movie Good Will Hunting. Here is a link Good Will Hunting Problem Reasoning if you want more information. The matrix T is equal to
the scalar z times the matrix shown below. I found the correct generating function for walks i to j which is S.
\begin{pmatrix} 0 & 1 & 0 & 1 \\ 1 & 0 & 2 & 1\\ 0 & 2 & 0 & 0\\ 1 & 1 & 0 & 0 \end{pmatrix}
How do we know
converges to zero?