Generalized Cayley-Hamilton-Newton identities

The q-generalizations of the two fundamental statements of matrix algebra - the Cayley-Hamilton theorem and the Newton relations - to the cases of qua ntum matrix algebras of RTT and Reflection-equation types have been obtaine d. We construct a family of matrix identities which we call Cayley-Hamilton -Newton identities and which underlie the characteristic identity as well a s the Newton relations for the RTT and Reflection equation algebras, in the sense that both the characteristic identity and the Newton relations are d irect consequences of the Cayley-Hamilton-Newton identities.