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The Commutation Matrices of Elements in Kronecker Quaternion Groups
Jambura Journal of Mathematics, 2022 This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers.
Yanita Yanita +2 more
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New Insight into Quaternions and Their Matrices
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2021 The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced.
Gülsüm Yeliz ŞENTÜRK +2 more
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Split quaternion matrices [PDF]
Miskolc Mathematical Notes, 2012 In this paper, we consider split quaternions and split quaternion matrices. Firstly, we give some properties of split quaternions. After that we investigate split quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of split quaternion matrices and we describe some of their properties. Furthermore, we give
Alagöz, Yasemin +2 more
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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 more
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Generalizing Frobenius inversion to quaternion matrices
Numerical Algorithms, 2023 Abstract In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient that other existing methods.
Qiyuan Chen 0001, Jeffrey Uhlmann, Ke Ye
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Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
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Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
Open Mathematics, 2021 In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
Hong Yan, Qi Feng
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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
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Low Rank Perturbations of Quaternion Matrices [PDF]
The Electronic Journal of Linear Algebra, 2017 Low rank perturbations of right eigenvalues of quaternion matrices are considered. For real and complex matrices it is well known that under a generic rank-$k$ perturbation the $k$ largest Jordan blocks of a given eigenvalue will disappear while additional smaller Jordan blocks will remain.
Mehl, Christian, Ran, Andre C.M.
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On the semicircular law of large dimensional random quaternion matrices [PDF]
, 2015 It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices.
Bai, Zhidong, Hu, Jiang, Yin, Yanqing
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