V2EX trivector

Trivector

释义 Definition

trivector(数学/几何代数):一种三阶(grade-3)多向量,可理解为由三个线性无关向量的外积(楔积)生成的量,用来表示有方向的三维体积元素(在三维空间里常与“伪标量”相关)。

发音 Pronunciation (IPA)

/travktr/

例句 Examples

A trivector can represent an oriented volume.
三向量可以表示一个有方向的体积。

In geometric algebra, the wedge product of three independent vectors forms a trivector that encodes the orientation and magnitude of a volume element.
在几何代数中,三个线性无关向量的楔积会形成一个三向量,用来编码体积元素的大小与取向。

词源 Etymology

tri-(“三”)+ vector(“向量”)构成,字面意思是“三(阶)的向量”。它来自外代数/几何代数的分级观念:向量是一阶,双向量(bivector)是二阶,三向量(trivector)是三阶。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Geometric Algebra for Physicists Chris Doran & Anthony Lasenby
  • Linear and Geometric Algebra Alan Macdonald
  • Clifford Algebra to Geometric Calculus David Hestenes & Garret Sobczyk
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