Solution
= Solution
The <transition matrix> is $P=(p_{ij})_{i,j\in S}$, where $p_{ij}=P(X_{n+1}=j\mid X_n=i)$. It is <stochastic matrix>[row-stochastic]: $p_{ij}\ge0$ and $\sum_jp_{ij}=1$ for each $i$. Initial states of zero probability can be specified by the chain's transition mechanism, so the <matrix> describes the chain from any starting state.