Research Information System
in: Pioneer and Academic Studies in Natural Science and Mathematics, İYİT NESLİHAN, Editor, All Sciences Academy Design, Konya, pp.5-14, 2025
In this section, operations in matrix theory are discussed. The contribution of the known operations in matrices, addition, subtraction and multiplication as well as division is analyzed. The relation of this operation in other fields and the new results obtained are presented. For example, the relation of matrices to special sequences and the relation of these sequences to each other are shown. Similarity and equivalence issues in matrix theory and the contribution of the operation are studied. The new results obtained are presented. New results with linear matrix equation systems and division are presented. In addition, the concept of transpose in matrices and the existence of new results between division in detail are introduced. New results of multiplication in matrices are obtained using division. Some of these results are that a regular matrix has infinite factors and every regular matrix can be written in terms of another regular matrix. The existence of some known properties in rational numbers was also investigated in matrices. The new features obtained were presented. The property of simplification and expansion in rational numbers is also provided in rational matrices. Finally, considering the multiplication and division property of matrices, the “POLOID” structure was created. Many properties related to this structure have been investigated.