Research On Calculation And Application In Matrix Equation Of The Generalized Inverse Matrices

The Generalized inverse matrices have got many conclusions, and its applications are extensive. Matrices are indispensable basic tools in natural sciences engineering techniques and social science, so the applications of the generalized inverse matrices are very extensive. Generally speaking, the generalized inverse matrices may be used in the field in which matrices are used. The research of the generalized inverse matrices is more thorough, the application of the generalized inverse matrices is more extensive. Many problems in the field of statistics of mathematics,linear programming,economics,numerical value analysis,automatic control,electronic net and mapping require the generalized inverse matrices to resolve. The generalized inverse matrices are indispensable studying tools in the least-square problems, the rectangular or ill-linear problems, the nonlinear problems, the non-constrained or constrained linear programming problems, control and identification of system problems, electronic net problems and so on.In the paper, we research the calculation and application of the generalized inverse matrices, and settle following problems:1. Based on the property of the generalized inverse matrices, we find out a new method to compute the generalized inverse matrices by soluting the matrix equation; We give a method to compute the Moore-Penrose inverse of the full-row matrix; In addition, we analyze the computational complexity of three common methods of computing the generalized inverse matrices.2. We compute the generalized inverse matrices of the Anti-symmetric matrix and the normal matrix.3. With the Moore-Penrose inverse, we research the matrix equation AX=XW in the space of SR^n×n and SR_P^n×n, and give the sufficient and necessary condition for the existence and the form of solution.4. With the generalized {1,3}- inverse, we research the solution and the squares solution of the matrix equation AX=B in the space of SR^n×n, SR_P^n×n and SAR_P^n×n.5. With the Moore-Penrose inverse, we research the matrix equation(?)in the space of S and S_P.6. With the Moore-Penrose inverse, we research the matrix equationX^H AX = A, and give its solution. where A is a Hermite matrix.