A Swift Introduction to Geometric Algebra

problem with classic geometry

  • different representation/operation in different dimension.
  • only has cross product in 3d space.

multi-vector

see the video for details.

geometric product

Definition of geometric product (understanding with reference to complex number):

\[\vec{u}\vec{v} = \vec{u} \cdot \vec{v} + \vec{u} \wedge \vec{v} = \|\vec{u} \| \|\vec{v} \|e^{i\theta}\]

闲谈

世界是由感性活动建立的，观念并不是理性展开的，而是人的实践中构建的。