This document provides a mathematical summary of quaternion algebra and calculus and how they relate to rotations and interpolation of rotations. The ideas are based on the article [1].

Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra. pacs 03.65.Bz, 03.65.Ca,11.15.Kc, 02.30.+g 1 Quaternion Quantum Mechanics Quantum mechanics defined over general algebras have been conjectured since 1934 [1]. In 1936 Birkoff and von Neumann noted that the p...

The traditional methods for representing forward kinematics of manipulators have been the homogeneous matrix in line with the D-H algorithm. In this paper a new method known as quaternion algebra is described and it is used for three dimensional representation and orientation in robot kinematics. This method is compared with homogeneous transform in terms of easiness of representation, computat...

Quaternion is an extension of the complex number system. are discovered by formulating 4 points in 4-dimensional vector space using cross product between two standard vectors. algebra over a field with bases and elements members field. Each element quaternion has inverse, despite fact that ring not commutative. Based on this, purpose this study to obtain characteristics split determine how it i...

The quaternion Fourier transform (QFT), which is a nontrivial generalization of the real and complex Fourier transform (FT) using quaternion algebra has been of interest to researchers for some years (see e.g. [3, 5]). It was found that many FT properties still hold but others have to be modified. Based on the (right-sided) QFT, one can extend the classical wavelet transform (WT) to quaternion ...

Let A be a definite quaternion algebra over ℚ, with discriminant D , and