Results 21 to 30 of about 542 (165)
Axioms, 2023 Quaternion is a four-dimensional and an extension of the complex number system. It is often viewed from various fields, such as analysis, algebra, and geometry.
Alit Kartiwa +3 more
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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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Some Results On Quaternion 3-Space
Cumhuriyet Science Journal, 2018 In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, withentries in a quaternion F-algebra Q, that are symmetric with respect to thecanonical involution Jγ is studied.
Atilla Akpınar, Fatma Özen Erdoğan
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IEEE Access, 2023 The processing of color images is of great interest, because the human perception of color is a very complex process, still not well understood. In this article, firstly the authors present an analysis of the well-known mathematical methods used to model
Eduardo Bayro-Corrochano +2 more
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A Convolution Theorem Related to Quaternion Linear Canonical Transform
Abstract and Applied Analysis, 2019 We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion convolution in the QLCT domain
Mawardi Bahri, Ryuichi Ashino
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Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +3 more
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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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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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IEEE Access, 2022 We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements.
Johannes Poppelbaum, Andreas Schwung
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Quad-Quaternion MUSIC for DOA Estimation Using Electromagnetic Vector Sensors
EURASIP Journal on Advances in Signal Processing, 2008 A new quad-quaternion model is herein established for an electromagnetic vector-sensor array, under which a multidimensional algebra-based direction-of-arrival (DOA) estimation algorithm, termed as quad-quaternion MUSIC (QQ-MUSIC), is proposed.
Xiaofeng Gong, Zhiwen Liu, Yougen Xu
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