General n-Dimensional Rotations

Antonio Aguilera       Ricardo Pérez-Aguila

Centro de Investigación en Tecnologías de Información y Automatización (CENTIA)

Universidad de las Américas, Puebla (UDLAP)

Ex-Hacienda Santa Catarina Mártir

México 72820, Cholula, Puebla


This paper presents a generalized approach for performing general rotations in the n-Dimensional Euclidean space around any arbitrary (n-2)-Dimensional subspace. It first shows the general matrix representation for the principal n-D rotations. Then, for any desired general n-D rotation, a set of principal n-D rotations is systematically provided, whose composition provides the original desired rotation. We show that this coincides with the well-known 2D and 3D cases, and provide some 4D applications.


Geometric Reasoning, Topological and Geometrical Interrogations, 4D Visualization and Animation.