Block partitioned representations for the drazin inverse of anti-triangular matrices and its applications

This thesis is organized in five parts. In the first chapter, a short introduction is given by mentioning the purpose of the thesis study. In the second chapter, the basic definitions, theorems and some general informations that will be required in our study are expressed. Also, the definition and some properties of Moore-Penrose inverse for a matrix and are listed. In the third chapter, it is given the definition of the Drazin inverse of a matrix and considered some properties of this inverse. Furthermore, some computational methods and several applications of the Drazin inverses of matrices are and block partitioned representations for the Drazin inverse of anti-triangular matrices are given in this chapter. In the fourth chapter, conclusions and recommendations are given. In the fifth chapter, the references used in the thesis are listed.