I have got the following transition matrix:
$A = \begin{pmatrix} p & 1-p \\ 1-q & q \end{pmatrix}$
How can one use the jordan normal form to get a closed-form to calculate such a values $A^n_{i,j}$ ?
I have got the following transition matrix:
$A = \begin{pmatrix} p & 1-p \\ 1-q & q \end{pmatrix}$
How can one use the jordan normal form to get a closed-form to calculate such a values $A^n_{i,j}$ ?
You find $P$ and $B$ such that $B$ is in Jordan form and $A=PBP^{-1}$. Then you find a formula for $A^n$ involving $B^n$, and take the advice of Rasmus from the comments.