Define the Standard Model gauge group to be S ( U ( 2) × U ( 3)), the subgroup of SU ( 5) consisting of block diagonal matrices with a 2 × 2 block and then a 3 × 3 block. (This is isomorphic to the ...
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an ...
Abstract: The recently developed quaternion Fourier transform (QFT) based on quaternion algebra has been found useful for color image processing and signal analysis. However, due to the noncommutative ...
IN a recent number of this Journal (p. 151) Mr. McAulay puts certain questions to Mr. Heaviside and to me, relating to a subject of such importance as to justify an answer somewhat at length. I cannot ...
ABSTRACT: In this paper, from the spacetime algebra associated with the Minkowski space ℝ 3,1 by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion ...
Abstract: In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion ...
Some of the methods in Rotation have docs that sound somewhat copy-pasted from similar quaternion code. For example, from_basis_unchecked: In order to get a valid unit-quaternion, the input must be an ...
This paper proposes a robust dual-quaternion based H-infinity task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous ...
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