Factorizations and eigenvalues of the generalized fibonacci matrices

This thesis consists of six chapters. In the first chapter, general information about the concepts used in the thesis is given. In the second chapter, the purpose and scope of the study are given, and in addition, an extensive literature review is made on the topics that form the basis of the thesis, existing studies are examined and the information obtained from these studies is synthesized. In the third chapter, the factorizations of matrices consisting of the generalized higher--order Fibonacci sequences are obtained. The decomposition processes of the matrices are carried out using various analytical methods and mathematical techniques, and the findings obtained in this process are presented in detail. In the fourth chapter, the lower and upper bounds of the eigenvalues of higher--order symmetric Fibonacci matrices are examined with the help of majorization theory and doubly stochastic matrices. In the fifth chapter, some numerical results are presented in order to show the accuracy and reliability of the theoretical findings obtained in the previous sections. In the sixth section, conclusions and suggestions regarding the thesis are given.