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We introduce the concept of reflexive moment functional in two variables andthe definition of reflexive orthogonal polynomial system. Also reverse matricesand their interesting algebraic properties are studied. Reverse matrices andreflexive polynomial systems are directly connected in the context of bivariateorthogonal polynomials. Centrosymmetric matrices, reverse matrices and theirconnections with reflexive orthogonal polynomial systems are presented.Finally, several particular cases and examples are analysed.

Centrosymmetric and reverse matrices in bivariate orthogonal polynomials