Results 191 to 200 of about 9,570 (204)

Algebraic techniques for diagonalization of a split quaternion matrix in split quaternionic mechanics

Journal of Mathematical Physics, 2015
In the study of the relation between complexified classical and non-Hermitian quantum mechanics, physicists found that there are links to quaternionic and split quaternionic mechanics, and this leads to the possibility of employing algebraic techniques of split quaternions to tackle some problems in complexified classical and quantum mechanics.
Tongsong Jiang, Ziwu Jiang, Zhaozhong Zhang   +2 more
openaire   +2 more sources

Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)

Mathematical Methods in the Applied Sciences, 2021
This paper provides two direct methods for solving the split quaternion matrix equation whereXis an unknown split quaternionη‐Hermitian matrix, andA, B, C, D, E, Fare known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore–Penrose generalized inverse, real representation, and complex representation of split ...
Ming‐Zhao Li, Shi‐Fang Yuan, Hua Jiang   +2 more
openaire   +1 more source

$${2\times 2}$$ 2 × 2 Matrix Representation Forms and Inner Relationships of Split Quaternions

Advances in Applied Clifford Algebras, 2019
This paper proposes a $${2\times 2}$$ real matrix isomorphic representation form of split quaternions and a $${2m\times 2n}$$
Qiu-Ying Ni, Jin-Kou Ding, Xue-Han Cheng, Ying-Nan Jiao   +3 more
openaire   +1 more source

Least squares X=±X^η* solutions to split quaternion matrix equation AXA^η*=B

Mathematical Methods in the Applied Sciences, 2019
In the paper, the split quaternion matrix equation AXAη*=B is considered, where the operator Aη* is the η‐conjugate transpose of A, where η∈{i,j,k}. We propose some new real representations, which well exploited the special structures of the original matrices. By using this method, we obtain the necessary and sufficient conditions for AXAη*=B to have X=
Xin Liu, Yang Zhang
openaire   +1 more source

Singular Value Decomposition of Dual Split Quaternion Matrix and Its Algorithm

Mathematical Methods in the Applied Sciences
ABSTRACTIn the theoretical study of dual split quaternions, the singular value decomposition of dual split quaternion matrix plays an important role. In this paper, we propose the dual number matrix representation of dual split quaternion and give the theory of singular value decomposition of the dual split quaternion matrix under ‐conjugate transpose.
Xiaochen Liu, Ying Li, Jianhua Sun, Ruyu Tao   +3 more
openaire   +1 more source

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 convenient research tools than quaternions.
Zi‐Han Gao, Qing‐Wen Wang, Lv‐ming Xie   +2 more
openaire   +1 more source

The (anti-) η -Hermitian solution to a novel system of matrix equations over the split quaternion algebra1

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 convenient research tools than quaternions.
Qing-Wen Wang, Zi-Han Gao, Lv-ming Xie
openaire   +1 more source

A Note on Matrix Representations of Split Quaternions

Journal of Advanced Research in Applied Mathematics, 2015
openaire   +1 more source

Color Image Recovery Using Low-Rank Quaternion Matrix Completion Algorithm

IEEE Transactions on Image Processing, 2022
Jifei Miao, Kit Ian Kou
exaly  

On Eigenvalues of Split Quaternion Matrices

Advances in Applied Clifford Algebras, 2013
Melek Erdoğdu, Mustafa Özdemİr
exaly