Moore_Penrose Inverse Of Partitioned Matrices And Its Application In The System Of Linear Equations

The method to solve linear equations using the inverse matrix is only feasible when the coefficient matrix is reversible. But for the general system of linear equations, the coefficient matrix may be a irreversible matrix or a rectangular matrix, in this case, we can not use this method to solve the system of linear equations. In order to find solutions of this system, we promote the inverse matrix to generalized inverse matrix, and than use the generalized inverse matrix to solve the system of linear equations.The generalized inverse matrix is important in many area, such as Data analysis, Multivariate analysis, Signal processing, System theory, Modern control theory, Network theory and so on. This paper studies the definition, properties, calculation of the generalized inverse matrix, and the applications in soluting the system of linear equations. Utilizing the generalized inverse matrix, we study the soluting of the general system of linear equations and the minimum norm solution.