Transition Matrix - Yousef's Notes
Transition Matrix

Transition Matrix

The [[matrix]] Q containing for each row the transition probabilities for a specific state is called the transition matrix.

$$ Q = \begin{pmatrix} 0.8 & 0.2 \\ 0.7 & 0.3 \end{pmatrix} $$
  • The matrix $Q$ is always a square matrix.
  • Each of its rows must add up to one.
  • All its entries are non-negative.
  • The entry $(i,j)$ is the probability of going from state $i$ to state $j$.

$$ Q = \begin{pmatrix} 0 & 0.3 & 0.7 \\ 0.1 & 0.9 & 0 \\ 0 & 0.4 & 0.6 \end{pmatrix} $$
  • [[n-Step Transition Probability]]