V2EX stochastic matrix

Stochastic Matrix

定义 Definition

随机矩阵(更常见指“随机/概率转移矩阵”):一个矩阵中元素都为非负数,并且每一行每一列的元素之和等于 1。常用于表示概率分布的变化或马尔可夫链的状态转移。
(注:行和为 1 的常叫 row-stochastic;列和为 1 的常叫 column-stochastic。)

发音 Pronunciation (IPA)

/stkstk metrks/

例句 Examples

A stochastic matrix describes the probabilities of moving from one state to another.
随机矩阵描述了从一个状态转移到另一个状态的概率。

Given a stochastic matrix, we can compute the long-run behavior of a Markov chain by analyzing its stationary distribution.
给定一个随机矩阵,我们可以通过分析其平稳分布来计算马尔可夫链的长期行为。

词源 Etymology

stochastic 来自希腊语 stokhastikos,意为“善于猜测/推测的”,后来在数学与统计语境中引申为“与随机性、概率有关的”。matrix 源自拉丁语 matrix(“母体、来源”),在数学中指用行列排列的数表。两者结合的 stochastic matrix 就指“用于表示随机(概率)结构的矩阵”。

相关词 Related Words

文学与著作 Literary Works

  • Andrey Markov《Investigation of a Remarkable Case of Dependent Trials》(研究依赖试验的经典论文传统中,引出用矩阵表达转移概率的框架)
  • William Feller《An Introduction to Probability Theory and Its Applications》(概率论经典教材,讨论马尔可夫过程与转移结构)
  • Sheldon M. Ross《Introduction to Probability Models》(常用教材,马尔可夫链章节常以随机矩阵表示转移概率)
  • Gilbert Strang《Linear Algebra and Its Applications》(线性代数教材中涉及非负矩阵、特征值与相关应用背景)
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