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Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
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Right linear map preserving the left spectrum of 2x2 quaternion matrices; pp. 378–386 [PDF]
Proceedings of the Estonian Academy of Sciences, 2018 In this paper, the form of a right linear map preserving the left spectrum of quaternion matrices of order 2 is characterized. The obtained conclusion is different from the classical results of the linear map preserving eigenvalues of complex matrices.
Deyu Duan +3 more
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A survey on the computation of quaternions from rotation matrices [PDF]
, 2019 The parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, 3D image processing, computer graphics, etc.
Sarabandi, Soheil, Thomas, Federico
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Abstract and Applied Analysis, 2013 The matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory.
Ning Li, Qing-Wen Wang
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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 +2 more
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Permanental processes from products of complex and quaternionic induced Ginibre ensembles [PDF]
, 2014 We consider products of independent random matrices taken from the induced Ginibre ensemble with complex or quaternion elements. The joint densities for the complex eigenvalues of the product matrix can be written down exactly for a product of any fixed ...
Akemann, G., Ipsen, J. R., Strahov, E.
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Journal of Applied Mathematics, 2014 Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the
Shi-Fang Yuan
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Ninety-Six Distinct Real Matrices for Representing a Quaternion Number
Journal of Mathematics, 2020 In this paper, we investigate on the number of all possible real matrices representing a quaternion number as three 4×4 skew-symmetric matrices plus the identity matrix of order 4, and how to determine these matrices.
W. E. Ahmed
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Review of Quaternion-Based Color Image Processing Methods
Mathematics, 2023 Images are a convenient way for humans to obtain information and knowledge, but they are often destroyed throughout the collection or distribution process.
Chaoyan Huang, Juncheng Li, Guangwei Gao
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Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales
Open Mathematics, 2020 In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex ...
Li Zhien, Wang Chao
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