CHOUIREB, MARWA2023-10-122023-10-122022https://dspace.univ-ghardaia.edu.dz/xmlui/handle/123456789/6548In this thesis, we establish necessary and sufficient conditions for the existence of the (P; Q) generalized reflexive (anti-reflexive) solutions and the common (P; Q) generalized reflexive (antireflexive) solutions to linear matrix equations AX = B and the system AX = B, XC = D respectively, with respect to the generalized reflection matrix dual (P; Q). Moreover, for all these solutions, we derive the explicit expression of the best solution estimator to a given matrix in the Frobenius norm(P; Q) generalized reflexive solution, (P; Q) generalized anti-reflexive solution, Matrix equation, Moore-penrose generalized inverse, Frobenius norm, generalized reflection matrix.Thesis