Generalized reflexive and anti-reflexive solutions of $$AX=B$$ A X = B

Abstract

In this paper, we establish some new conditions for the existence and the representations for the $$(P, Q)$$(P,Q) generalized reflexive and anti-reflexive solutions to matrix equation $$AX = B$$AX=B with respect to the generalized reflection matrix dual $$(P, Q)$$(P,Q). Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided.