arXiv subjects

Mahmoud Saad Mehany

Publications and source records attributed to Mahmoud Saad Mehany.

3 recordsLinked to original sources

arXiv2023

Algebraic conditions and general solution to a system of quaternion tensor equations with applications

This paper investigates the necessary and sufficient algebraic conditions to a constrained system of Sylvester-type quaternion tensor equations. An explicit formula of the general solution regarding the Moore-Penrose inverses of some block given tensors is obtained. As an application of a particular case, we establish the solvability conditions and the general solution to a system of Sylvester-type quaternion tensor equations involving $η$-Hermitian unknowns. An algorithm with a numerical example is proposed to compute the general solution of the main system.

math.RA↗

arXiv2023

A new generalization of a system of two-sided coupled Sylvester-like quaternion tensor equations

This study establishes consistency conditions and a general solution for a coupled system that consists of five two-sided Sylvester-like tensor equations in ten quaternion variables throughout the Einstein tensor product. Certain specific cases are thus established. In a direct application, we investigate certain necessary and sufficient conditions for the existence of an $η$-Hermitian solution to five coupled two-sided Sylvester-like quaternion tensor equations. Finally, we present an algorithm and a numerical example to validate the main result.

math.RA↗

arXiv2022

A Sylvester-type matrix equation over the Hamilton quaternions with an application

We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves $η$-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.

math.RA↗