A stochastic matrix, also called a probability matrix, probability transition matrix, transition matrix, substitution matrix, or Markov matrix, is matrix used to characterize transitions for a finite Markov chain, Elements of the matrix must be real numbers in the closed interval [0, 1]. A completely independent type of stochastic matrix is defined as a square matrix with entries in a field F such that the sum of elements in each column equals 1. There are two nonsingular 2×2 stochastic matrices over Z_2 (i.e., the integers mod 2), [1 | 0 0 | 1] and [0 | 1 1 | 0].
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