Related papers: Tetranacci and Tetranacci-Lucas Quaternions
In this paper we review the topological model for the quaternions based upon the Dirac string trick. We then extend this model, to create a model for the octonions - the non-associative generalization of the quaternions.
The purpose of the paper is to construct a new representation of dual quaternions called bi$-$periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual…
The Cayley-Dickson algebras R (real numbers), C (complex numbers), H (quaternions), O (octonions), S (sedenions), and T (trigintaduonions) have attracted the attention of several mathematicians and physicists because of their important…
In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
In this paper, the third-order Jacobsthal generalized quaternions are introduced. We use the well-known identities related to the third-order Jacobsthal and third-order Jacobsthal-Lucas numbers to obtain the relations regarding these…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
In this study, we apply the binomial transforms to Tribonacci and Tribonacci-Lucas sequences. Also, the Binet formulas, summations, generating functions of these transforms are found using recurrence relations. Finally, we illustrate the…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence…
A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three time-like coordinates, we have been able to consistently recover a suitable formulation of…
Starting from some ideas given by Bales in [Ba; 09], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley-Dickson process. As a consequence of this result, we prove that an…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
The algebra of fourvectors is described. The fourvectors are more appropriate than the Hamilton quaternions for its use in Physics and the sciences in general. The fourvectors embrace the 3D vectors in a natural form. It is shown the…
In this paper, we define Gaussian generalized Tetranacci numbers and as special cases, we investigate Gaussian Tetranacci and Gaussian Tetranacci-Lucas numbers with their properties.