Abstract
We obtain new representations for the general positive and real-positive solutions of the equation axa*=c in a C*-algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA*=C for operators between Hilbert spaces and for finite matrices are given.
Acknowledgement
The authors are indebted to the referee whose careful reading of the article helped to eliminate several mistakes, and to improve the presentation of the article.