V2EX bistochastic

Bistochastic

定义 Definition

bistochastic(双随机的):在数学中通常指双随机矩阵的性质一个方阵的每个元素都非负,并且每一行的和与每一列的和都等于 1。(在不同语境下也可写作 doubly stochastic。)

例句 Examples

A bistochastic matrix has nonnegative entries and each row sums to 1.
双随机矩阵的元素都非负,并且每一行的和都等于 1。

By Birkhoff’s theorem, every bistochastic matrix can be written as a convex combination of permutation matrices.
根据伯科夫定理,每个双随机矩阵都可以表示为若干置换矩阵的凸组合。

发音 Pronunciation (IPA)

/bastokstk/

词源 Etymology

bi- 表示“二、双”,stochastic 源自希腊语 stokhos(“目标、猜测”之意,后引申为“随机/概率”相关)。合在一起,bistochastic 用来强调“在两个方向(行与列)都满足随机/归一化约束”的性质,因此常对应中文“双随机”。

相关词 Related Words

文学与著作中的用例 Literary & Notable Works

  • R. A. Brualdi, Combinatorial Matrix Theory(组合矩阵论著作中系统讨论双随机矩阵与相关结构)
  • Albert W. Marshall, Ingram Olkin, Barry C. Arnold, Inequalities: Theory of Majorization and Its Applications(在“主序/主化”理论中频繁出现双随机矩阵作为核心工具)
  • Persi Diaconis, Bernd Sturmfels, “Algebraic algorithms for sampling from conditional distributions”(统计与代数方法中涉及双随机/列联表与相关构造)
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