The common Hermitian solution to the system of matrix equations $B_{i}XB_{i}^{\ast}=A_{i}, i=1, 2, 3$

Abstract

In this paper, a new solvability condition and the explicit expression of the common Hermitian solutions (CHSs) to the system of matrix equations $B_{i}XB_{i}^{\ast}=A_{i}, i=1, 2, 3$ are deduced by using the Moore-Penrose inverses and some matrix decompositions. Finally, a numerical example is provided to validate the accuracy of the results.