On r-min and r-max matices and their properties

In this thesis, r-min and r-max matrices, which are the general forms of min and max matrices, are defined such that min and max matrices are obtained for r=1 in these matrices. In the first part, matrix theory and number theory were mentioned and the studies in the literature were listed. The next chapter is devoted to the basic definitions and theorems utilized throughout the thesis. In the third chapter, in which the basic results we obtained about r-min and r-max matrices are given, in addition to the determinant, inverse, norm and factorization of these matrices, linear algebraic properties are also obtained for Hadamard inverses. Finally, these theoretical results were coded in the Maple 18 program and compared with the program's own results and found to be provided. For numerical examples of the obtained results, r-min and r-max matrices, whose entries are Fibonacci numbers and hyperharmonic Fibonacci numbers, are taken and their determinants, inverses and norms are shown.