Results 1 to 10 of about 666,240 (259)
Symmetry, 2023 In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the η-anti-Hermitian solution to a system of constrained matrix equations over the ...
Bai-Ying Ren +2 more
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Pose consensus based on dual quaternion algebra with application to decentralized formation control of mobile manipulators [PDF]
Journal of the Franklin Institute, 2019 This paper presents a solution based on dual quaternion algebra to the general problem of pose (i.e., position and orientation) consensus for systems composed of multiple rigid-bodies.
Adorno, Bruno V. +3 more
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Consimilarity and quaternion matrix equations AX −^X B = C, X − A^X B = C
Special Matrices, 2014 L. Huang [Consimilarity of quaternion matrices and complex matrices, Linear Algebra Appl. 331(2001) 21–30] gave a canonical form of a quaternion matrix with respect to consimilarity transformationsA ↦ ˜S−1AS in which S is a nonsingular quaternion matrix ...
Klimchuk Tatiana, Sergeichuk Vladimir V.
doaj +3 more sources
IEEE Access, 2021 Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics, computer science, and engineering. This review presents a comprehensive study of works on Quaternion Algebra and GA applications in computer science and engineering ...
E. Bayro-Corrochano
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A novel color images security-based on SPN over the residue classes of quaternion integers $$\:\varvec{H}{\left(\mathbb{Z}\right)}_{\varvec{\pi\:}}$$ [PDF]
Scientific ReportsThe exponential growth of multimedia data transmission has intensified the demand for advanced image encryption systems capable of resisting contemporary cryptanalytic attacks while maintaining computational efficiency.
Muhammad Sajjad, Nawaf A. Alqwaifly
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Characteristic of Quaternion Algebra Over Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space
Muhammad Faldiyan +2 more
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RSVD for Three Quaternion Tensors with Applications in Color Video Watermark Processing
Axioms, 2023 In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of ...
Wen-Juan Chen, Shao-Wen Yu
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Quaternion and Split Quaternion Neural Networks for Low-Light Color Image Enhancement
IEEE Access, 2023 In this study, two models of multilayer quaternionic feedforward neural networks are presented. Whereas the first model is based on quaternion algebra, the second model uses split quaternion algebra.
Eduardo Jesus De Davila-Meza +1 more
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Dynamics of Mobile Manipulators using Dual Quaternion Algebra [PDF]
Journal of Mechanisms and Robotics, 2020 This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are propagated through
F. F. A. Silva +2 more
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Partial Differential Equations in Applied Mathematics, 2023 This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation
Muhammad Afdal Bau +4 more
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