The general common nonnegative-definite and positive-definite solutions to the matrix equations \(AXA^ *=BB^ *\) and \(CXC^ *=DD^ *\).
The authors 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 \(CXC^*=DD^*\). In the case of existence they give the representation of the general common solution of this type. The paper is supplementary to this one of \textit{D. M. Young}, \textit{J. W. Seaman} and \textit{L. M. Meaux} [J. Multivariate Anal. 68, 165--175 (1999; Zbl 0927.62057)] after a mistake in the latter paper has been indicated by \textit{J. Groß} [Linear Algebra Appl. 321, 123--129 (2000; Zbl 0984.15011)]. The authors present an example illustrating the advantage of their approach.
scientific article; zbMATH DE number 2138620