  This paper provides a general operadic definition for the notion of splitting
the operations of algebraic structures. This construction is proved to be
equivalent to some Manin products of operads and it is shown to be closely
related to Rota-Baxter operators. Hence, it gives a new effective way to
compute Manin black products. The present construction is shown to have
symmetry properties. Finally, this allows us to describe the algebraic
structure of square matrices with coefficients in algebras of certain types.
Many examples illustrate this text, including the case of Jordan algebras.
