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New solvability conditions yield common Hermitian solutions in multiple matrix equations, implying novel problem-solving approaches.
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 X B_i^* = 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 obtained results.
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Zhang et al. (2025) studied this question.
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