Natural Geometry of Nonzero Quaternions

Riemannian L Averaging on the Lie Group of Nonzero Quaternions

This paper discusses quaternion L geometric weighting averaging working on the multiplicative Lie group of nonzero quaternionsH∗, endowed with its natural bi-invariant Riemannian metric. Algorithms for computing the Riemannian L center of mass of a set of points, with 1 ≤ p ≤ ∞ (i.e., median, mean, L barycenter and minimax center), are particularized to the case of H∗. Two different approaches ...

Differential Geometry of the q-Quaternions

Differential calculus on the quantum quaternionic group GL(1, Hq) is introduced. E-mail: [email protected]

ILLUSTRATIONS FROM GEOMETRY OF THE THEORY OF ALGEBRAIC QUATERNIONS By

On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry

Conway and Smith’s book is a wonderful introduction to the normed division algebras: the real numbers (R), the complex numbers (C), the quaternions (H) and the octonions (O). The first two are well-known to every mathematician. In constrast, the quaternions and especially the octonions are sadly neglected, so the authors rightly concentrate on these. They develop these number systems from scrat...

Quaternions and Biquaternions: Algebra, Geometry and Physical Theories

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and ”tensor” formulation of Q-units with their possible representations are discussed and groups of Q-units transformations leaving Q-multiplication rule form-invariant are determined. A series of mathematical and physical applications is offered, among...