THROUGH A GENERALIZED INVERSE
Czesław Stępniak · Demonstratio Mathematica · 2008
Traditionally, the existence of a generalized inverse of a matrix A is derived in an indirect way from the matrix equation AXA = A. We reach this result in a direct and constructive manner, based on spectral decomposition.Moreover, some new results on its characterization and on representation of the entire set of generalized inverses are given.Usefulness of these results is demonstrated in examples.