- For a matrix whose elements are stochastic, see Random matrix
In
mathematics, a
stochastic matrix (also termed
probability matrix,
transition matrix,
substitution matrix, or
Markov matrix) is a
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 in
probability theory,
statistics,
mathematical finance and
linear algebra, as well as
computer science and
population genetics. There are several different definitions and types of stochastic matrices:
- A right stochastic matrix is a real square matrix, with each row summing to 1.
- A left stochastic matrix is a real square matrix, with each column summing to 1.
- A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1.