Abstract
The matrix equation AX=B with PX=XP and XH=sX constraints is considered, where P is a given Hermitian involutory matrix and s=±1. By an eigenvalue decomposition of P, we equivalently transform the constrained problem to two well-known constrained problems and represent the solutions in terms of the eigenvectors of P. Using Moore–Penrose generalized inverses of the products generated by matrices A, B and P, the involved eigenvectors can be released and eigenvector-free formulas of the general solutions are presented. Similar strategy is applied to the equations AX=B, XC=D with the same constraints.
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