In probability theory, a transition rate matrix (also known as an 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 (sometimes written A) element qij (for i ≠ j) denotes the rate departing from i and arriving in state j. Diagonal elements qii are defined such that and therefore the rows of the matrix sum to zero (see condition 3 in the definition section).