Calculation of generalized inverses of real matrices using matlab 7.5 and application to those linear matrix equations

In the first chapter of the work, the historical evolution of generalized inverse concept is summarized.In the Chapter 2, some concepts and theorems that will be the fundamental tools for the Chapter 3 and Chapter 4 are given.In the Chapter 3, a general theory about the linear equation system is mentioned. The analytic solutions to the problem of finding the vector , from among the general solution set of the system if it is consistent, and from among the least squares solution set of the system if it is inconsistent, such that the norm of is minimum for a given vector are established.In the Chapter 4, a general theory about the linear matrix equation is first presented. Then, the analytic solutions to the problems of finding the matrix , from among the general solution set of the system if it is consistent, and from among the least squares solution set of the system if it is inconsistent, such that Frobenius norm of is minimum for a given matrix are established. Morever, it is also given analytic solutions about some special cases, studied in the literature recently, of the problem considered in this work.To explain theoretical results given in the Chapter 2, 3, and 4, the algorithms are constructed and the numerical examples are given using MATLAB 7.5. To be able to make comparison of acquired results, the examples in Chapter 4 are especially taken as examples that are available in literature.