A matrix P ∈ Rn×n is said to be a symmetric orthogonal matrix if P = P T = P−1. A matrix A ∈ Rn×n is said to be generalized centro-symmetric (generalized central anti-symmetric )with respect to P , if A = PAP (A = −PAP ). In this paper, an iterative method is constructed to solve the generalized centrosymmetric solutions of a linear matrix equation AXB + CY D = E, with real pair matrices X and ...