对于元素为随机的矩阵，参见随机矩阵

在数学中，随机矩阵（也称为概率矩阵、转移矩阵、 替代矩阵、或马尔可夫矩阵）是用来描述一个马尔可夫链的转变的矩阵 。它的每一项都是一个表示概率的非负实数。它适用于概率论、统计学和线性代数，也在计算机科学和群体遗传学中使用。 有几种不同的定义和类型随机矩阵：

同理，可以定义随机矢量（也称为概率矢量）为元素为非负实数且和为1的矢量。因此，右随机矩阵的每一行（或左随机矩阵的每一列）都是一个随机矢量。

在英语数学文献中的惯例是用概率的行矢量和概率的右随机矩阵，而不用列矢量和左随机矩阵，本文遵循此惯例。

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: