The current study investigates the solvability conditions and general solution of three symmetrical systems coupled Sylvester-like quaternion matrix equations. Accordingly, necessary sufficient for consistency these are determined, solutions thereby deduced. An algorithm a numerical example constructed over quaternions to validate results this paper.

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

This paper presents a unified algorithm for solving the forward displacement problem of in-parallel Stewart-Gough platforms (SGPs), i.e., the connection joints are not restricted to lie in a plane. The novelty of this paper lies in that the new algorithm is versatile and robust for in-parallel SGPs. In this paper, we classify all in-parallel SGPs into five cases in terms of the number of soluti...

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved. Moreover, we give a set of invertible elements in split quaternion algebras and in split octonion algebras.

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre’ s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.

In this paper, a quaternion firefly algorithm is utilized to solve a multi-row facility layout design problem with the objective of minimizing the total cost of transportation. A quaternion firefly algorithm takes the motion of the firefly as a quaternion one. Consequently, the solution space is explored more accurately and the answers are of higher quality. That is, the answers are considerabl...

In this study, we develop a general method to solve the linear elliptic quaternionic matrix equations by means of real representation quaternion matrices. A pseudocode for our approach that provides solution is expressed. Moreover, apply well-known Slyvester and Kalman Yakubovich over algebra.

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...