Stochastic Matrix

What is a Stochastic Matrix?

A stochastic matrix is a square matrix of non-negative real numbers in a closed interval that list the probabilities in a finite Markov chain. This is 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. These square matrices can take multiple forms, depending on which stochastic vector (row or column) can be summed to 1.

  • A right stochastic matrix has each row summing to 1.

  • A left stochastic matrix has each column summing to 1.

  • A doubly stochastic matrix has both rows and columns summing to 1.