I have been given the adjacency matrix
$$A = \begin{pmatrix} 0 & 1 & 0&1&1 \\ 1 & 0 &1&1& 0\\ 0& 1 &0&0&1 \\1&1&0&0&1 \\0&1&1&0&0\\\end{pmatrix}$$ And I have been asked to find the H-matrix and the page rank vector
I found the H-matrix to be $$\begin{pmatrix} 0 & 1/3 & 0&1/3&1/3 \\ 1/3 & 0 &1/3&1/3& 0\\ 0& 1/2 &0&0&1/2 \\1/3&1/3&0&0&1/3 \\0&1/2&1/2&0&0\\\end{pmatrix}$$
I know that to the page rank vector is found from $r_{n} = r_{0}H^n$ where $$r_{0} = \begin{pmatrix}\frac{1}{5}&\frac{1}{5}&\frac{1}{5}&\frac{1}{5}&\frac{1}{5}\end{pmatrix}$$ in this case
So to get $r_{n}$, I need to find $L = \lim_{n \to \infty} H^{n} $ then the page rank vector is $$ r_{n} = r_{0}L$$
I am not sure how to calculate this limit in order to find the page rank vector What is the best way to find the limit for the matrix H ?i.e $\lim_{n \to \infty} H^{n}$