In mathematics, a stochastic matrix (also termed probability matrix, transition matrix, substitution matrix, or Markov matrix ) is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century. There are several different...