V2EX bivector

Bivector

Definition|释义

bivector(双向量/二向量):在几何代数(Geometric Algebra)或外代数中表示“有方向的面积元素”的量,通常可看作由两个向量的外积(wedge product)组成,例如 \(a \wedge b\)。它常用于描述平面、旋转、角动量等与“平面方向”相关的概念。(在不同数学体系中也可能有更广义的用法。)

Pronunciation|发音(IPA)

/bavktr/

Examples|例句

A bivector can represent an oriented plane segment.
双向量可以表示一个带方向的平面“面积片段”。

In geometric algebra, the rotation of a vector is often expressed using an exponential of a bivector.
在几何代数中,向量的旋转常用双向量的指数形式来表达。

Etymology|词源

由前缀 bi-(“二、双”)+ vector(“向量”)构成,字面意思是“两(个向量相关的)向量量”。该词在外代数与几何代数的发展语境中常用,用来强调它对应“由两个向量生成的平面量/面积量”。

Related Words|相关词汇

Literary Works|文学/经典著作中的出现

  • David Hestenes, **New Foundations for Classical Mechanics**(讨论几何代数中双向量与旋转等概念)
  • Chris Doran & Anthony Lasenby, **Geometric Algebra for Physicists**(系统使用 bivector 表示平面量与旋转生成元)
  • Alan Macdonald, **Linear and Geometric Algebra**(面向学习者讲解 bivector 与外积、几何意义)
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