Results 11 to 20 of about 653,122 (340)
Characteristic of Quaternion Algebra Over Fields [PDF]
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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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 ...
Qing-Wen Wang, Wang Qing-Wen
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A System of Coupled Two-sided Sylvester-type Tensor Equations over the Quaternion Algebra
Taiwanese Journal of Mathematics, 2020 We establish some necessary and sufficient conditions for the solvability to a system of a pair of coupled two-sided Sylvester-type tensor equations over the quaternion algebra.
Qing-Wen Wang
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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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Quaternion group algebra and representations of the quaternions [PDF]
Communications in Algebra, 2019 AbstractIn this paper, we provide a concrete and explicit decomposition of the quaternion group algebra through a suitable basis of the algebra.
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Free groups in quaternion algebras
Journal of Algebra, 2013 10 pages, article presented in conferences: Algebra School, Brasilia-Brazil, Brasilia National University (july-2010); Summer 2009 Meeting of CMS in Groups and Hopf Algebras section, St. Jonh's-Canada, Memorial University of Newfoundland (June-2009); Groups, Rings and Group Rings, Ubatuba-Brazil (july-2008)
Juriaans, S.O., Souza Filho, A.C.
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ComputersIn this paper, we describe the associative and commutative algebra or the (2,2)-model of quaternions with application in color image enhancement. The method of alpha-rooting, which is based on the 2D quaternion discrete Fourier transform (QDFT) is ...
Artyom M. Grigoryan, Alexis A. Gomez
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Quaternion constituents of group algebras [PDF]
Proceedings of the American Mathematical Society, 1971 In this paper it is shown that each quaternion division algebra central over the rationals appears as a division ring constituent of some rational group algebra.
Mark Benard
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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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