Results 281 to 290 of about 653,122 (340)

The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra

Linear and multilinear algebra, 2020
In this paper, we investigate the least-squares solution with the least norm to the following system of tensor equations over quaternions where are unknown quaternion tensors and the others are given quaternion tensors. Using the expressions of the Moore-
Qing-Wen Wang, Ru-Yuan Lv, Yang Zhang
semanticscholar   +1 more source

On the quaternionic Weyl algebra

Advances in Applied Clifford Algebras, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
SABADINI, IRENE MARIA, D. Struppa
openaire   +4 more sources

On some mod p representations of quaternion algebra over ℚp

Compositio Mathematica
Let $F$ be a totally real field in which $p$ is unramified and let $B$ be a quaternion algebra over $F$ which splits at at most one infinite place. Let $\overline {r}:\operatorname {{\mathrm {Gal}}}(\overline {F}/F)\rightarrow \mathrm {GL}_2(\overline ...
Yongquan Hu, Haoran Wang
semanticscholar   +1 more source

Quaternion Algebras

1999
No abstract.
Ivanyos, G., Rónyai, L.
openaire   +2 more sources

The (anti‐) η‐Hermitian solution to a novel system of matrix equations over the split quaternion algebra

Mathematical methods in the applied sciences
In comparison to quaternions, split quaternions exhibit a more intricate algebraic structure, characterized by the presence of nontrivial zero factors. Furthermore, in various fields such as geometry and electromagnetism, split quaternions serve as more ...
Zi-Han Gao, Qing‐Wen Wang, Lv-Ming Xie
semanticscholar   +1 more source

Quaternion algebras

, 2017
This thesis deals with quaternion algebras. A quaternion algebra is a four dimensional vector space with basis 1, i, j, k and multiplication defined as i2 = a, j2 = b, ij = -ji = k.
Bečka, Pavel
core   +3 more sources

Derivations of generalized quaternion algebra

Turkish Journal of Mathematics, 2019
The purpose of this paper is to determine derivations of the algebra Hα,β of generalized quaternions over the reals and hence to obtain the algebra Der(Hα,β) of derivations of Hα,β .
E. Kizil, Y. Alagöz
semanticscholar   +1 more source

The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle

, 2019
This article aims to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform. We study some fundamental properties of this extension such as scaling, translation, rotation, and Parseval’s identity,
Y. El Haoui
semanticscholar   +1 more source

Quaternion Algebras I

2003
One of the main aims of this chapter is to complete the classification theorem for quaternion algebras over a number field by establishing the existence part of that theorem. This theorem, together with other results in this chapter, make use of the rings of adeles and groups of ideles associated to number fields and quaternion algebras.
Colin Maclachlan, Alan W. Reid
openaire   +1 more source

Geometric techniques for robotics and HMI: Interpolation and haptics in conformal geometric algebra and control using quaternion spike neural networks

Robotics Auton. Syst., 2018
In this work, by reformulating screw theory (generalization of quaternions) in the conformal geometric algebra framework, we address the interpolation, virtual reality, graphics engineering, haptics.
E. Bayro-Corrochano, L. Lechuga-Gutiérrez, M. Garza-Burgos   +2 more
semanticscholar   +1 more source