Transition-rate matrix
In probability theory, a transition-rate matrix (also known as a Q-matrix, intensity matrix, or infinitesimal generator matrix) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states. In a transition-rate matrix Q {\displaystyle Q} (sometimes written A {\displaystyle A} ), element q i j {\displaystyle q_{ij}} (for i ≠ j {\displaystyle i\neq j} ) denotes the rate departing from i {\displaystyle i} and arriving in state j {\displaystyle j} .