V2EX geometric algebra

Geometric Algebra

定义 Definition

几何代数:一种把向量、复数、四元数、外代数(楔积)等统一到同一套语言中的代数体系,用来以坐标更少、几何意义更直观的方式描述旋转、反射、面积/体积方向量、以及物理中的空间与时空变换。(在不同语境下也常与 Clifford algebra/克利福德代数 密切相关。)

发音 Pronunciation (IPA)

/dimtrk ldbr/

例句 Examples

Geometric algebra can represent rotations in a very compact way.
几何代数可以用非常简洁的方式表示旋转。

In robotics and physics, geometric algebra provides a unified framework that can simplify calculations involving vectors, planes, and transformations.
在机器人学和物理学中,几何代数提供了一个统一的框架,能简化涉及向量、平面与变换的计算。

词源 Etymology

Geometric 来自希腊语 geōmetria(“测量土地/几何学”,由 “土地” + metron“度量”构成);algebra 来自阿拉伯语 al-jabr(“复原、补全”,早期用于指代方变形与求解的方法)。合在一起,geometric algebra 字面上可理解为“用于几何对象与几何变换的代数方法”。

相关词 Related Words

文学与名著作品 Literary Works

  • David Hestenes New Foundations for Classical Mechanics(以几何代数重建经典力学的表述框架)
  • Chris Doran & Anthony Lasenby Geometric Algebra for Physicists(面向物理学应用的代表性教材)
  • Alan Macdonald Linear and Geometric Algebra(将线性代数与几何代数并行讲解的入门书)
  • David Hestenes Space-Time Algebra(用几何代数语言讨论狭义相对论与时空几何)
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