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Blade Products and Angles Between Subspaces
Advances in Applied Clifford Algebras ( IF 1.5 ) Pub Date : 2021-09-21 , DOI: 10.1007/s00006-021-01169-w
André L. G. Mandolesi 1
Affiliation  

Principal angles are used to define an angle bivector of subspaces, which fully describes their relative inclination. Its exponential is related to the Clifford geometric product of blades, gives rotors connecting subspaces via minimal geodesics in Grassmannians, and decomposes giving Plücker coordinates, projection factors and angles with various subspaces. This leads to new geometric interpretations for this product and its properties, and to formulas relating other blade products (scalar, inner, outer, etc., including those of Grassmann algebra) to angles between subspaces. Contractions are linked to an asymmetric angle, while commutators and anticommutators involve hyperbolic functions of the angle bivector, shedding new light on their properties.



中文翻译:

子空间之间的叶片积和角度

主角用于定义子空间的角双向量,它完全描述了它们的相对倾角。它的指数与叶片的 Clifford 几何乘积有关,通过 Grassmannians 中的最小测地线给出转子连接子空间,并分解给出 Plücker 坐标、投影因子和具有各种子空间的角度。这导致对该乘积及其属性的新几何解释,以及将其他叶片乘积(标量、内、外等,包括格拉斯曼代数)与子空间之间的角度相关联的公式。收缩与不对称的角度有关,而换向器和反换向器涉及角度双向量的双曲线函数,揭示了它们的性质。

更新日期:2021-09-21
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