Results 11 to 20 of about 120 (109)

Dual Fibonacci Quaternions [PDF]

Advances in Applied Clifford Algebras, 2014
In this study, we define the dual Fibonacci quaternion and the dual Lucas quternion. We derive the relations between the dual Fibonacci and the dual Lucas quaternion which connected the Fibonacci and the Lucas numbers. Furthermore, we give the Binet and Cassini formulas for these quaternions.
Nurkan, Semra Kaya, Güven İ.A.
openaire   +4 more sources

On Fibonacci quaternion matrix [PDF]

Notes on Number Theory and Discrete Mathematics, 2021
In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.
Serpil Halici, Ömür Deveci
openaire   +3 more sources

On Generalized Fibonacci Quaternions and Fibonacci-Narayana Quaternions [PDF]

Advances in Applied Clifford Algebras, 2013
Accepted in Adv. in Appl.
Flaut, Cristina, Shpakivskyi, Vitalii
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Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
openaire   +1 more source

New Properties and Identities for Fibonacci Finite Operator Quaternions

Mathematics, 2022
In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions.
Nazlıhan Terzioğlu, Can Kızılateş, Wei-Shih Du   +2 more
doaj   +1 more source

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients.
Halici Serpil, Cerda-Morales Gamaliel
doaj   +1 more source

Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties [PDF]

Notes on Number Theory and Discrete Mathematics
The primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence ...
Faruk Kaplan, Arzu Özkoç Öztürk
doaj   +1 more source

On Fibonacci Quaternions [PDF]

Advances in Applied Clifford Algebras, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices

Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2019
In this paper, we consider one of the most knownFibonacci matrix Qand the Fibonacciquaternion matrix MQFn, where Qnis the n-th Fibonacci quaternion.In particular we define some new quaternion matrices.
Bahar Demirtürk Bitim
doaj   +1 more source

New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
doaj   +1 more source