Results 41 to 50 of about 245,475 (190)
Visualizing Quaternion Multiplication
IEEE Access, 2017 Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it
Jongchan Baek +3 more
doaj +1 more source
Linear Algebra and its Applications, 1984 Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect ...
openaire +2 more sources
IEEE Access, 2021 For scenarios of coherent underwater sources at low signal-to-noise ratio (SNR), a novel quaternion-based DOA algorithm without eigendecomposition is proposed using a linear vector-hydrophone array.
Yi Lou +3 more
doaj +1 more source
The 2-refined neutrosophic quaternions numbers [PDF]
Neutrosophic Sets and SystemsThis paper explores the concept of 2-refined neutrosophic quaternion numbers by first introducing their formal definition along with the notion of equality between two such numbers.
Iqbal Ahmed Musa +2 more
doaj +1 more source
Modified Hand–Eye Calibration Using Dual Quaternions
Applied Sciences, 2022 This paper presents a modified model for hand–eye calibration based on dual quaternion algebra. By using dual quaternions to represent the rotations and translations of a rigid body simultaneously in the task space, the formulation is elegant for the ...
Guozhi Li +3 more
doaj +1 more source
Fractal and Fractional, 2023 Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has ...
Călin-Adrian Popa
doaj +1 more source
Selectivity in quaternion algebras
Journal of Number Theory, 2012 We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\mathfrak A$ satisfies the Eichler condition; that is, there exists an archimedean prime of $K$ which does not ramify in $\mathfrak A$. Let
openaire +2 more sources
On the linkage of quaternion algebras
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2002 Let \(B\) and \(C\) be quaternion algebras over a field \(F\). A well known theorem [\textit{A. A. Albert}, Proc. Am. Math. Soc. 35, 65-66 (1972; Zbl 0263.16012), \textit{C.-H. Sah}, J. Algebra 20, 144-160 (1972; Zbl 0226.15010)] states that \(B\otimes_FC\) is a division algebra if and only if \(B\) and \(C\) have no common quadratic splitting field ...
openaire +3 more sources
Superderivations and Jordan superderivations of generalized quaternion algebras [PDF]
Journal of Mahani Mathematical ResearchLet $H_{\alpha,\beta}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to consider superderivations and Jordan superderivations of $H_{\alpha,\beta}$ and hence to obtain the superalgebra $Der_{s} (H_{\alpha,\beta})$
Leila Heidari Zadeh
doaj +1 more source
Contractions on ranks and quaternion types in clifford algebras
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element.
Dmitry S Shirokov
doaj +1 more source