The general common nonnegative-definite and positive-definite solutions to the matrix equations AXA∗ = BB∗ and CXC∗ = DD∗ Original Research Article

We give necessary and sufficient conditions for the existence of a common nonnegative-definite (positive-definite) solution to the pair of matrix equations AXA∗ = BB∗ and CXC∗ = DD∗, and derive a representation of the general common nonnegative-definite (positive-definite) solution to these two equations when they have such common solutions. This paper can be viewed as a supplementary version of that derived by Young et al. [1] since Groβ [2] has given a counterexample to point out a mistake in their basic Theorem 1. The presented example shows the advantage of the proposed approach.