On the Solutions of Some Linear Complex Quaternionic Equations

Some complex quaternionic equations in the type AX-XB= C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtaine

A Note on the Solutions of Some Linear Octonionic Equations

The main concerns of this paper are the linear equations with one term and one unknown of the forms: a(xa) =r, a(xb ) = r and (ax)b =r, and the linear equations with two terms and one unknown of the forms: (ax)b +(g x)d =r and a (xb )+g (xd ) =r over the octonion field. Explicit general solutions of the equations in forms a(xa) = r, a(xb ) = r and (ax)b = r are given, and solutions of the octonionic equations form (ax)b +(g x)d = r and a (xb )+g (xd ) = r by matrix representation of octonions are derived using some particular cases. Examples of numerical equations are considered

On the solutions of the quaternion interval systems [x]=[A] [x]+ [b]

WOS:000342265700032It is known that linear matrix equations have been one of the main topics in matrix theory and its applications. The primary work in the investigation of a matrix equation (system) is to give solvability conditions and general solutions to the equation(s). In the present paper, for the quaternion interval system of the equations defined by [x] = [A][x] + [b], where [A] is a quaternion interval matrix and [b] and [x] are quaternion interval vectors, we derive a necessary and sufficient criterion for the existence of solutions [x]. Thus, we reduce the existence of a solution of this system in quaternion interval arithmetic to the existence of a solution of a system in real interval arithmetic. (C) 2014 Elsevier Inc. All rights reserved

On pell quaternions and pell-lucas quaternions

WOS:000370339300004The main object of this paper is to present a systematic investigation of new classes of quaternion numbers associated with the familiar Pell and Pell-Lucas numbers. The various results obtained here for these classes of quaternion numbers include recurrence relations, summation formulas and Binet's formulas

On Jacobsthal and Jacobsthal-Lucas Octonions

WOS:000396095300002Various families of quaternion and octonion number sequences (such as Fibonacci quaternion, Fibonacci octonion, and so on) have been established by a number of authors in many different ways. In addition, formulas and identities involving these number sequences have been presented. In this paper, we aim at establishing new classes of octonion numbers associated with the familiar Jacobsthal and Jacobsthal-Lucas numbers. We introduce the Jacobsthal octonions and the Jacobsthal-Lucas octonions and give some of their properties. We derive the relations between Jacobsthal octonions and Jacobsthal-Lucas octonions