Results 21 to 30 of about 47,407 (236)

On quaternionic functional analysis [PDF]

, 2006
In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the ...
Agrawal, Agrawal, Biedenharn, CHI-KEUNG NG, Horwitz, Horwitz, Horwitz, Horwitz, Kulkarni, Kulkarni, Lance, Ng, Suhomlinov, Torgasev, Torgasev, Torgasev, Torgasev, Viswanath   +17 more
core   +2 more sources

Coarse Alignment Technology on Moving base for SINS Based on the Improved Quaternion Filter Algorithm

Sensors, 2017
Initial alignment of the strapdown inertial navigation system (SINS) is intended to determine the initial attitude matrix in a short time with certain accuracy.
Tao Zhang, Yongyun Zhu, Feng Zhou, Yaxiong Yan, Jinwu Tong   +4 more
doaj   +1 more source

Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised $\mathbb{HR}$ Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator

Machines, 2022
This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function ...
Kazuhiko Takahashi, Eri Tano, Masafumi Hashimoto   +2 more
doaj   +1 more source

Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers

Journal of Mathematics, 2023
In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
doaj   +1 more source

An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications

Journal of Applied Mathematics, 2014
This paper, by means of complex representation of a quaternion matrix, discusses the consimilarity of quaternion matrices, and obtains a relation between consimilarity and similarity of quaternion matrices.
Tongsong Jiang, Xuehan Cheng, Sitao Ling
doaj   +1 more source

Signal flow graph and control of realizable autonomous nonlinear Chen model with quaternion variables

Alexandria Engineering Journal, 2020
In this work, we continue our study of autonomous nonlinear dynamical systems with quaternion variables. We present a novel chaotic Chen system with quaternion variables. This system in real form is high (nine) dimensional.
Emad E. Mahmoud, M. Higazy, Turkiah M. Al-Harthi   +2 more
doaj   +1 more source

Generalised quadratic forms and the u-invariant [PDF]

, 2017
The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and
Dolphin, Andrew
core   +2 more sources

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

IEEE Access, 2022
We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements.
Johannes Poppelbaum, Andreas Schwung
doaj   +1 more source

Rotacija z enotskim kvaternionom ( = Rotation with unit quaternion) [PDF]

Geodetski Vestnik, 2014
A quaternion is a hyper-complex number. A rule for quaternion multiplications allows us to use it as a rotation in three-dimensional space. The aim of this article is to present quaternion rotations to the Slovene professional geodetic public ...
Klemen Kregar, Mitja Lakner, Dušan Kogoj   +2 more
doaj   +1 more source

Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers

IEEE Photonics Journal, 2015
A method to structure the Jones quaternion utilizing Pauli matrices is proposed, improving the quaternion theory of polarization optics. It is proved that the Stokes quaternion is the double product of the Jones quaternion and its Hermitian transpose and
Lanlan Liu, Chongqing Wu, Chao Shang, Zhengyong Li, Jian Wang   +4 more
doaj   +1 more source