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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]

Notes on Number Theory and Discrete Mathematics
This paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
doaj   +1 more source

Quaternion feedback attitude control system design based on weighted–L2–gain performance

Results in Engineering, 2023
The operation and accomplishment of a satellite's mission depend on its capacity to control its attitude. A rotation matrix parameterization, such as a (unit) quaternion, is frequently used to represent the attitude information needed for attitude ...
Harry Septanto, Edi Kurniawan, Djoko Suprijanto   +2 more
doaj   +1 more source

Matrix representation of quaternions

Linear Algebra and its Applications, 2003
The authors establish that there are 48 distinct triples of real \(4\times 4\) signed permutation matrices \(H,K,L\), subject to the well known conditions \(HH=-I\), \(HJ=K\) etc., which together with the identity matrix \(I\) will serve as a basis in the regular representation of the real quaternions.
Farebrother, Richard William, Groß, Jürgen, Troschke, Sven-Oliver   +2 more
openaire   +2 more sources

Quaternion Filtering Based on Quaternion Involutions and its Application in Signal Processing

IEEE Access, 2019
The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized HR calculus, the quaternion ...
Gang Wang, Rui Xue
doaj   +1 more source

Developing a Static Kinematic Model for Continuum Robots Using Dual Quaternions for Efficient Attitude and Trajectory Planning

Applied Sciences, 2023
Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory ...
Yunfei Li, Qiuhao Wang, Qian Liu
doaj   +1 more source

Quaternion Discrete Fourier Transform-Based Color Image Watermarking Method Using Quaternion QR Decomposition

IEEE Access, 2020
In this paper, a new Quaternion Discrete Fourier Transform (QDFT)-based digital color image watermarking method is presented. In addition, the Quaternion QR (QQR) decomposition is applied in digital watermarking technology for the first time.
Mianjie Li, Xiaochen Yuan, Hai Chen, Jianqing Li   +3 more
doaj   +1 more source

Hermitian Solutions to a Quaternion Matrix Equation

, 2011
In this paper, we consider Hermitian and skew-Hermitian solutions to a certain matrix equation over quaternion algebra H. Necessary and sufficient conditions are obtained for the quaternion matrix equation to have Hermitian and skew-Hermitian solutions ...
Wen Feng Wang, Ning Li, Jing Jiang
core   +1 more source

Some New Properties of The Real Quaternion Matrices and Matlab Applications

Cumhuriyet Science Journal, 2019
In this study, firstly, it was shown that the set of real quaternionmatrices is a -dimensional module over the real matrix ring and -dimensional module over the complex matrix ring .
Kemal Gökhan Nalbant, Salim Yüce
doaj   +1 more source

A New Method of Solving Special Solutions of Quaternion Generalized Lyapunov Matrix Equation

, 2022
In this paper, we study the bisymmetric and skew bisymmetric solutions of quaternion generalized Lyapunov equation. With the help of semi-tensor product of matrices, some new conclusions on the expansion rules of row and column of matrix product on ...
Ying Li, Wenxv Ding, Xueling Fan, Zhihong Liu   +3 more
core   +1 more source

Ranks of a Constrained Hermitian Matrix Expression with Applications

Journal of Applied Mathematics, 2013
We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expression C4−A4XA4∗ where X is a Hermitian solution to quaternion matrix equations A1X=C1, XB1=C2, and A3XA3*=C3.
Shao-Wen Yu
doaj   +1 more source