GENERALIZED INVERSE: PROPERTIES, REPRESENTATIONS AND APPLICATIONS

A growing interest in the theory of generalized inverses and in applications of generalized inverses in such fields as engineering and statistics has stimulated an interest in teaching about generalized inverses in linear algebra courses. When A is a nonsingular matrix, the equation Ax=b has a unique solution.The generalized inverse of a singular matrix can be motivated as generalization of this situation. In fact, the solution will be the unique solution to Ax=b when a unique solution exists, will be a solution when there is more than one solution, and will be a least squares solution when no solution exists. Generalized inverse can also be applied to network theory and in optimizing problems. Beside this, generalized inverse can be represented by contour integrations. We can directly calculate generalized inverse by the special Mathematica command PseudoInverse.