An Algebraic Approach to n-Plithogenic Square Matrices For
Noor Edin Rabeh1, Othman Al-Basheer2, Sara Sawalmeh3, Rozina Ali
Baghdad University, College of Science, Baghdad, Iraq
Sudan University Of Science and Technology, Faculty Of Science, Khartoum, Sudan
Mutah University, Faculty of Science, Mutah, Jordan
Cairo University, Department of Mathematics, Cairo, Egypt
Emails: edinnoori45@gmail.com; othmanzolbasheer@gmail.com; Sarahsawalmeh98@gmail.com
Abstract
This paper is dedicated to study the algebraic properties and substructures that are related to the symbolic 18 and 19 plithogenic square matrices, where we present many different theorems and examples to clarify the computation of symbolic 18 and 19 plithogenic determinants, and finding 18-plithogenic and 19-plithogenic eigenvalues and eigenvectors. On the other hand, we provide algorithms for computing the inverses of symbolic 18-plithogenic and 19-plithogenic matrices with necessary and sufficient conditions for the orthogonality of those matrices.
Keywords: symbolic 18-plithogenic matrix; symbolic 19-plithogenic matrix; eigenvalue; eigenvector; orthogonal matrix