Akademik Veri Yönetim Sistemi
10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, Kırklareli, Türkiye, 6 - 08 Ocak 2024, ss.58-62
This study is about division in matrices and eigenvalues-eigenvectors. The concept of eigenvalues-eigenvectors in the literature is discussed. The status of division operation on these concepts is analyzed. The eigenvalues and eigenvectors of the elements forming the division are compared with the result. The matrix resulting and the resulting difference are investigated. The eigenvalues-eigenvectors of the constituent matrices the division and the eigenvalueseigenvectors obtained from the result matrix are examined. The brief literature review of the study is written and the summary history of this study is added in the first section. The theorems related to the subject are listed. Some applications related to this topic are given. The preliminary information that will form the second part is given. The new developments and findings are investigated in the next section. The changes of known definitions, theorems and lemmas are observed. If there are unprotected cases, examples are given for these situations. The new contributions on the parallel cases of matrix product and scalar product in the eigenvalue definition are investigated. The important hints that will contribute to transformations are obtained. The concept of rotation in the planes in the studies is concluded carried to higher dimensions with this contribution. The rotation in the plane is realized only in two directions. There is no direction limit in dimension 3. This situation covers matrices larger than order 3rd. The computation of parallel states corresponding to the same eigenvalue is expected to be of new interest. In short, the study marks the beginning of innovations between multiplication-division and eigenvalue-eigenvector.