Results 11 to 20 of about 1,018 (285)

Quaternion Algebras [PDF]

Graduate Texts in Mathematics, 2021
This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader,
John Voight
exaly   +7 more sources

Smoothing method for unit quaternion time series in a classification problem: an application to motion data [PDF]

Scientific Reports, 2023
Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a
Elena Ballante, Lise Bellanger, Pierre Drouin, Silvia Figini, Aymeric Stamm   +4 more
doaj   +2 more sources

Hypercomplex neural networks: Exploring quaternion, octonion, and beyond in deep learning [PDF]

MethodsX
Hypercomplex Neural Networks (HNNs) represent the next frontier in deep learning, building on the mathematical theory of quaternions, octonions, and higher-dimensional algebras to generalize conventional neural architectures.
Raghavendra M Devadas, Vani Hiremani, Preethi, Sowmya T, Sapna R, Praveen Gujjar   +5 more
doaj   +2 more sources

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   +2 more sources

Superderivations and Jordan superderivations of generalized quaternion algebras [PDF]

Journal of Mahani Mathematical Research
Let $H_{\alpha,\beta}$ 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   +2 more sources

Quaternion algebras

, 2017
This thesis deals with quaternion algebras. A quaternion algebra is a four dimensional vector space with basis 1, i, j, k and multiplication defined as i2 = a, j2 = b, ij = -ji = k.
Bečka, Pavel
core   +3 more sources

Rotations and units in quaternion algebras

Journal of Number Theory, 2012
Unit groups of orders in quaternion algebras over number fields provide important examples of non-commutative arithmetic groups.
Corrales-Rodrigáñez, Capi, Capi Corrales-Rodrigáñez, Corrales Rodrigáñez, Carmen   +2 more
exaly   +2 more sources

Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023
Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors  and .
Muhammad Faldiyan, Ema Carnia, Asep Kuswandi Supriatna   +2 more
doaj   +1 more source

Quaternion-based machine learning on topological quantum systems

Machine Learning: Science and Technology, 2023
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the complexity in
Min-Ruei Lin, Wan-Ju Li, Shin-Ming Huang
doaj   +1 more source

Some properties of orders of quaternion algebras with regard to the discrete norm [PDF]

Mathematica Bohemica, 2016
Quaternion algebras $(\frac{-1,b}{\mathbb{Q}})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Jan Horníček, Miroslav Kureš, Lenka Macálková   +2 more
doaj   +1 more source