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 $$A^n_{i,j}$$ ?
2026-04-09 16:57:08.1775753828
Get the closed-form using jordan normal form?
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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.