The common Hermitian solution to the system of matrix equations Bᵢ X Bᵢ^* = Aᵢ, i = 1, 2, 3

Key Points

• The research aims to establish a new condition for the solvability of matrix equations and to derive explicit common Hermitian solutions.
• Utilized Moore-Penrose inverses and matrix decompositions to derive solutions.
• Deduced new solvability conditions for the system of equations.
• Provided a numerical example to demonstrate the results.
• Achieved explicit expressions for common Hermitian solutions to the equations B_i X B_i^* = A_i for i = 1, 2, 3.
• Established effective methods for solving matrix equations using the new conditions.