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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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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 +4 more
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Reachability problems in quaternion matrix and rotation semigroups [PDF]
Information and Computation, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Paul Bell, Igor Potapov
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A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation
Abstract and Applied Analysis, 2014 A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equation X−AX^B=CY based on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient
Caiqin Song +3 more
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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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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]
Notes on Number Theory and Discrete MathematicsThis 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
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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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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 +2 more
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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
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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
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