Results 11 to 20 of about 8,815 (298)

A Unified Approach: Split Quaternions with Quaternion Coefficients and Quaternions with Dual Coefficients

Mathematics, 2020
This paper aims to present, in a unified manner, results which are valid on both split quaternions with quaternion coefficients and quaternions with dual coefficients, simultaneously, calling the attention to the main differences between these two ...
Fatih Yilmaz, Emel Karaca
exaly   +4 more sources

Pauli–Leonardo quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities ...
Zehra İşbilir, Mahmut Akyiğit, Murat Tosun   +2 more
doaj   +3 more sources

Quaternions and matrices of quaternions [PDF]

Linear Algebra and its Applications, 1997
The author gives a useful survey on quaternions and matrices of quaternions. He recalls standard facts going back to Rowan Hamilton as well as new results motivated by applications in physical theories. The main research problem presented in the paper is to extend the classical matrix theory from complex to the quaternion matrices.
Zhang, Fuzhen, Fuzhen Zhang
openaire   +4 more sources

On Pell Quaternions and Pell-Lucas Quaternions

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimen, Cennet Bolat, Ipek, Ahmet
openaire   +6 more sources

The Neutrosophic Quaternions Numbers [PDF]

Neutrosophic Sets and Systems
This article aims to study the neutrosophic quaternion numbers, where we defined the neutrosophic quaternions numbers and the two equal neutrosophic quaternions numbers, also, the neutrosophic quaternions numbers algebra were introduced by studying ...
Yaser Ahmad Alhasan, Basel Hamdo Alarnous, Iqbal Ahmed Musa   +2 more
doaj   +4 more sources

On the Lichtenberg hybrid quaternions [PDF]

Mathematica Moravica
In this study, we define Lichtenberg hybrid quaternions. We give the Binet's formula, the generating functions, exponential generating functions and sum formulas of these quaternions. We find some relations between Jacobsthal hybrid quaternions, Mersenne
Morales Gamaliel
doaj   +3 more sources

Hybrid Quaternions of Leonardo

Trends in Computational and Applied Mathematics, 2022
In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented.
M. C. S. Mangueira, F. R. V. Alves, P. M. M. C. Catarino   +2 more
doaj   +1 more source

Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions

Mathematics, 2022
We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions.
Ayşe Zeynep Azak
doaj   +1 more source

On Dual Quaternions with $k-$Generalized Leonardo Components

Journal of New Theory, 2023
In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo,
Gülsüm Yeliz Saçlı, Çiğdem Zeynep Yılmaz   +1 more
doaj   +1 more source

On Balancing and Lucas-balancing Quaternions [PDF]

, 2021
summary:The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas,
Patel, Bijan Kumar, Ray, Prasanta Kumar
core   +2 more sources