A new expression of the Hermitian solutions to a system of matrix equations with applications (Q2796974)

In the first part of this research article, the authors give a new necessary and sufficient condition for the existence of a Hermitian solution which was given earlier by \textit{C. G. Khatri} and \textit{S. K. Mitra} [SIAM J. Appl. Math. 31, 579--585 (1976; Zbl 0359.65033)], \textit{M. L. Arias} and \textit{M. C. Gonzalez} [Linear Algebra Appl. 433, No. 6, 1194--1202 (2010; Zbl 1200.47023)], \textit{Q. Wang} and \textit{C. Yang} [Commentat. Math. Univ. Carol. 39, No. 1, 7--13 (1998; Zbl 0937.15008)], \textit{C. R. Johnson} and \textit{M. Lundquist} [in: Operator theory and complex analysis. Proceedings of a workshop, held in Sapporo, Japan, June 11-14, 1991. Basel: Birkhäuser. 234--251 (1992; Zbl 0806.47010)], \textit{Q.-W. Wang} and \textit{C.-Z. Dong} [Linear Algebra Appl. 433, No. 7, 1481--1489 (2010; Zbl 1214.47015)], giving a suitable lemma. In the second part, the authors give a new expression of the general Hermitian solution to the system of matrix equations by giving some suitable theorems. In Parts 3 and 4, the authors give max-min ranks and inertias part of the general solution of this system with suitable theorems. This paper is written in very well manner.