Stochastic Matrix

Definition:

In mathematics, a stochastic 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 is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. 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

在数学上，随机矩阵Stochastic Matrix 是一个用于描述马尔科夫链转移的方阵，其每个元素都是一个非负实值，代表一个概率。 它也被称为 概率矩阵 Probability Matrix, 转移矩阵Transition Matrix, 替代矩阵 Substitution Matrix, 或者 马尔科夫矩阵 Markov Matrix.

Right stochastic matrix

Right stochastic matrix 是一个实值方阵，其每一行的和是1.

Left stochastic matrix

Left stochastic matrix 是一个实值方阵，其每一列的和是1.

Doubly stochastic matrix

Doubly stochastic matrix 是一个方阵，其行列的和均为1.

Permutation Matrix

Permutation Matrix， 置换矩阵，是一种特殊的Doubly stochastic matrix. 其元素是0与1，置换矩阵的每一行和每一列都恰好有一个1，其余元素都是0