V2EX transition matrix

Transition Matrix

定义 Definition

转移矩阵:在线性代数、概率论与马尔可夫链中,用一个矩阵表示“从一个状态转到另一个状态”的规则或概率。最常见的是马尔可夫链的转移概率矩阵:矩阵第 \(i\) 行第 \(j\) 列表示从状态 \(i\) 转移到状态 \(j\) 的概率(通常每一行加起来等于 1)。

发音 Pronunciation (IPA)

/trnzn metrks/

例句 Examples

A transition matrix shows the probability of moving from one state to another.
转移矩阵显示从一个状态移动到另一个状态的概率。

Given the transition matrix, we can predict the long-term distribution of the Markov chain by finding its stationary distribution.
给定转移矩阵,我们可以通过求平稳分布来预测该马尔可夫链的长期分布。

词源 Etymology

transition 源自拉丁语 transitio,意为“通过、转变”;matrix 源自拉丁语 matrix,原意为“母体、来源”,在数学中引申为“矩阵(元素的排列)”。合在一起,transition matrix 就是“用矩阵形式表达转变/转移关系(常为概率)”。

相关词 Related Words

文献与著作 Literary / Notable Works

  • Introduction to Probability Models Sheldon M. Ross
  • Markov Chains J. R. Norris
  • Pattern Recognition and Machine Learning Christopher M. Bishop
  • Reinforcement Learning: An Introduction Richard S. Sutton & Andrew G. Barto
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