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The matrix equations AX=B,XC=D with the constraint PX=sXP are considered, where P is a given Hermitian matrix satisfying P2=I and s=±1. Using an eigenvalue decomposition of P, the constrained problem can be equivalently transformed to two independent (unconstrained) problems of matrix equations in similar forms, and hence the constrained problem can be solved in terms of the eigenvectors of P. In...
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