Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}

实与复化 Clifford 代数中的 SVD 与极分解

On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

本文提出在任意维度与符号的非退化实与复化 Clifford 几何代数中，仅用代数运算实现任意多重向量的奇异值分解（SVD）与极分解，并定义了相关结构，为计算机科学、工程和物理等领域的应用提供基础。

射影几何代数中的简并性利用

Exploiting degeneracy in projective geometric algebra

本文深入研究射影几何代数所基于的简并克利福德代数的内部结构，利用分裂扩张实现元素分解，推导普莱费尔公理的起源，并证明该代数同构于扭平凡扩张。

Transposition anti-involution in Clifford algebras and invariance groups of scalar products on spinor spaces

We introduce on the abstract level in real Clifford algebras \cl_{p,q} of a non-degenerate quadratic space (V,Q), where Q has signature ε=(p,q), a transposition anti-involution \tp. In a spinor representation, the anti-involution \tp gives transposition, complex Hermitian conjugation or quaternionic Hermitian conjugation when the spinor space \check{S} is viewed as a \cl_{p,q}-left and \check{K}-right module with \check{K} isomorphic to R or R^2, C, or, H or H^2. \tp is a lifting to \cl_{p,q} of an orthogonal involution \tve: V \rightarrow V which depends on the signature of Q. The involution …

Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups

In this paper, we make the case that Clifford algebra is the natural framework for root systems and reflection groups, as well as related groups such as the conformal and modular groups: The metric that exists on these spaces can always be used to construct the corresponding Clifford algebra. Via the Cartan-Dieudonné theorem all the transformations of interest can be written as products of reflections and thus via `sandwiching' with Clifford algebra multivectors. These multivector groups can be used to perform concrete calculations in different groups, e.g. the various types of polyhedral grou…