The general common Hermitian nonnegative-definite solution to the matrix equations \(AXA=BB\) and \(CXC=DD\) with applications in statistics
The author obtains necessary and sufficient conditions for the solvability of the couple of matrix equations \(AXA^*=BB^*\) and \(CXC^*=DD^*\) where the solution \(X\) must be Hermitian nonnegative-definite. A representation of the general common such solution (when it exists) is given. Thus the author solves a statistical problem concerned when testing linear hypotheses about regression coefficients in the multivariate linear model. He corrects a result of \textit{D.M. Young, J.W. Seaman Jr.} and \textit{L.M. Meaux} [J. Multivariate Anal. 68, No.2, 165-175 (1999; Zbl 0927.62057)] which has been proved to be wrong in \textit{J. Groß} [Linear Algebra Appl. 321, 123-129 (2000; Zbl 0984.15011)].
Hermitian (symmetric) nonnegative-definite solution
Hermitian (symmetric) positive-definite solution
scientific article; zbMATH DE number 2167800